{"id":173,"date":"2026-06-07T02:22:42","date_gmt":"2026-06-07T02:22:42","guid":{"rendered":"https:\/\/physicsfundamentalsinfo.com\/blog\/?p=173"},"modified":"2026-06-07T02:22:43","modified_gmt":"2026-06-07T02:22:43","slug":"velocity-vs-speed","status":"publish","type":"post","link":"https:\/\/physicsfundamentalsinfo.com\/blog\/kinematics\/velocity-vs-speed\/","title":{"rendered":"Velocity vs Speed: What&#8217;s the Difference?"},"content":{"rendered":"\n<div class=\"pf-citation\"><div class=\"eyebrow\">Definition<\/div><p>\nVelocity vs speed comes down to direction: speed is a scalar measuring only how fast an object moves (distance \u00f7 time), while velocity is a vector measuring how fast and in what direction it moves (displacement \u00f7 time). Speed has magnitude only; velocity has magnitude and direction.\n<\/p><\/div>\n<p>Picture two runners who both finish a 400-metre lap in exactly 80 seconds. They ran at the same speed \u2014 yet if you ask where each one ended up relative to where they started, the answer is &#8220;nowhere.&#8221; That gap between how fast you move and where you actually end up is the whole story of speed versus velocity.<\/p>\n<p>It sounds like hair-splitting, but it decides real outcomes: whether a pilot reaches the right airport, why a satellite never falls despite never slowing down, and how your sat-nav guesses your arrival time. Get the distinction right once and a surprising amount of physics suddenly clicks into place.<\/p>\n<h2>What Is the Difference Between Speed and Velocity?<\/h2>\n<p>Start with the everyday meaning, then sharpen it. <strong>Speed<\/strong> answers one question \u2014 how fast? It is a <strong>scalar<\/strong>: a quantity with size but no direction, like temperature or mass.<\/p>\n<p><strong>Velocity<\/strong> answers two questions at once: how fast, and which way? That makes it a <strong>vector<\/strong> \u2014 a quantity carrying both a magnitude and a direction. The magnitude of an object&#8217;s velocity is simply its speed.<\/p>\n<p>So the relationship is tidy. Speed is the &#8220;how fast&#8221; part of velocity with the direction stripped away. A car doing 90 km\/h has a speed; the same car doing 90 km\/h due north has a velocity.<\/p>\n<p>One consequence trips up almost everyone. Because velocity has direction, it can be positive or negative, and it can cancel itself out \u2014 speed cannot. A reading of &#8220;\u22125 m\/s&#8221; is a velocity (5 m\/s in the negative direction); a speed is always just 5 m\/s.<\/p>\n<h2>The Speed and Velocity Formulas<\/h2>\n<p>Both quantities are built from a change in position over a change in time. But they disagree about what counts as &#8220;position change.&#8221;<\/p>\n<p>Average speed uses the total path length you actually travelled:<\/p>\n<div class=\"pf-formula\">average speed = total distance \/ total time<\/div>\n<p>Average velocity uses displacement \u2014 the straight-line change from start to finish, with direction:<\/p>\n<div class=\"pf-formula\">v = \u0394x \/ \u0394t<\/div>\n<p>Here every symbol has a job:<\/p>\n<ul>\n<li><strong>v<\/strong> \u2014 average velocity, a vector, measured in metres per second (m\/s).<\/li>\n<li><strong>\u0394x<\/strong> \u2014 displacement (the change in position, also a vector), measured in metres (m). The Greek \u0394 (&#8220;delta&#8221;) means &#8220;change in&#8221;.<\/li>\n<li><strong>\u0394t<\/strong> \u2014 the time interval, measured in seconds (s).<\/li>\n<li><strong>distance<\/strong> \u2014 total path length actually covered, in metres (m); always positive.<\/li>\n<\/ul>\n<p>Shrink the time interval to a single instant and you get <strong>instantaneous velocity<\/strong> \u2014 the value at one moment rather than averaged over a trip:<\/p>\n<div class=\"pf-formula\">v = lim (\u0394t \u2192 0) \u0394x \/ \u0394t = dx \/ dt<\/div>\n<p>That limit is the derivative of position with respect to time. Its magnitude is the instantaneous speed \u2014 the number a speedometer shows. The same definitions are laid out at <a href=\"http:\/\/hyperphysics.phy-astr.gsu.edu\/hbase\/vel2.html\" target=\"_blank\" rel=\"noopener\">HyperPhysics<\/a>, a long-standing university reference.<\/p>\n<h2>Speed vs Velocity: The Key Differences at a Glance<\/h2>\n<p>If you only remember one thing, remember this: speed throws away direction, velocity keeps it. Everything in the table below follows from that single fact.<\/p>\n<div class=\"pf-table-scroll\" style=\"display:block;width:100%;max-width:100%;overflow-x:auto;-webkit-overflow-scrolling:touch;margin:1.5em 0;\">\n<table style=\"width:100%;border-collapse:collapse;word-break:break-word;\">\n<thead>\n<tr style=\"background:#0A1628;color:#FAF6EE;\">\n<th style=\"padding:10px 12px;text-align:left;border:1px solid #D9CFB8;\">Feature<\/th>\n<th style=\"padding:10px 12px;text-align:left;border:1px solid #D9CFB8;\">Speed<\/th>\n<th style=\"padding:10px 12px;text-align:left;border:1px solid #D9CFB8;\">Velocity<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td style=\"padding:10px 12px;border:1px solid #D9CFB8;\"><strong>Type of quantity<\/strong><\/td>\n<td style=\"padding:10px 12px;border:1px solid #D9CFB8;\">Scalar<\/td>\n<td style=\"padding:10px 12px;border:1px solid #D9CFB8;\">Vector<\/td>\n<\/tr>\n<tr style=\"background:#F5F2EA;\">\n<td style=\"padding:10px 12px;border:1px solid #D9CFB8;\"><strong>What it tells you<\/strong><\/td>\n<td style=\"padding:10px 12px;border:1px solid #D9CFB8;\">How fast only (magnitude)<\/td>\n<td style=\"padding:10px 12px;border:1px solid #D9CFB8;\">How fast and in which direction (magnitude + direction)<\/td>\n<\/tr>\n<tr>\n<td style=\"padding:10px 12px;border:1px solid #D9CFB8;\"><strong>Based on<\/strong><\/td>\n<td style=\"padding:10px 12px;border:1px solid #D9CFB8;\">Distance travelled (total path length)<\/td>\n<td style=\"padding:10px 12px;border:1px solid #D9CFB8;\">Displacement (straight-line change in position)<\/td>\n<\/tr>\n<tr style=\"background:#F5F2EA;\">\n<td style=\"padding:10px 12px;border:1px solid #D9CFB8;\"><strong>Can it be negative?<\/strong><\/td>\n<td style=\"padding:10px 12px;border:1px solid #D9CFB8;\">No \u2014 always zero or positive<\/td>\n<td style=\"padding:10px 12px;border:1px solid #D9CFB8;\">Yes \u2014 a sign shows direction (in one dimension)<\/td>\n<\/tr>\n<tr>\n<td style=\"padding:10px 12px;border:1px solid #D9CFB8;\"><strong>Over a round trip<\/strong><\/td>\n<td style=\"padding:10px 12px;border:1px solid #D9CFB8;\">Average speed is greater than zero<\/td>\n<td style=\"padding:10px 12px;border:1px solid #D9CFB8;\">Average velocity is zero (displacement = 0)<\/td>\n<\/tr>\n<tr style=\"background:#F5F2EA;\">\n<td style=\"padding:10px 12px;border:1px solid #D9CFB8;\"><strong>SI unit &amp; symbol<\/strong><\/td>\n<td style=\"padding:10px 12px;border:1px solid #D9CFB8;\">metres per second (m\/s); written v or |v|<\/td>\n<td style=\"padding:10px 12px;border:1px solid #D9CFB8;\">metres per second (m\/s); written as a vector v (bold or with an arrow)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<h2>How Can Speed Stay Constant While Velocity Changes?<\/h2>\n<p>Here is the question that separates a memorised definition from real understanding. Can something move at a perfectly steady speed and still have a changing velocity? Yes \u2014 and it happens every time anything travels in a curve.<\/p>\n<p>Think of a car going round a roundabout at a constant 30 km\/h. The speedometer needle never moves. But the direction the car points \u2014 and therefore its velocity \u2014 is swinging round the whole time.<\/p>\n<p>Because velocity is changing, the car is accelerating, even though it is neither speeding up nor slowing down. That acceleration points toward the centre of the curve; physicists call it centripetal acceleration, and it is what you feel as the push toward the outside of a bend.<\/p>\n<svg viewBox=\"0 0 640 380\" role=\"img\" aria-label=\"An object moving counter-clockwise around a circular path with four equal-length velocity arrows drawn tangent to the circle, showing constant speed but changing velocity direction\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" style=\"width:100%;height:auto;max-width:640px;display:block;margin:1.5em auto;background:#F5F2EA;border-radius:6px;\">\n<text x=\"320\" y=\"34\" text-anchor=\"middle\" font-family=\"Manrope, Arial, sans-serif\" font-size=\"18\" font-weight=\"700\" fill=\"#7A1F2B\">Constant Speed, Changing Velocity<\/text>\n<circle cx=\"200\" cy=\"208\" r=\"105\" fill=\"none\" stroke=\"#0A1628\" stroke-width=\"2.5\" stroke-dasharray=\"6 7\"><\/circle>\n<circle cx=\"200\" cy=\"208\" r=\"3\" fill=\"#142139\"><\/circle>\n<circle cx=\"305\" cy=\"208\" r=\"7\" fill=\"#7A1F2B\"><\/circle>\n<circle cx=\"200\" cy=\"103\" r=\"7\" fill=\"#7A1F2B\"><\/circle>\n<circle cx=\"95\" cy=\"208\" r=\"7\" fill=\"#7A1F2B\"><\/circle>\n<circle cx=\"200\" cy=\"313\" r=\"7\" fill=\"#7A1F2B\"><\/circle>\n<line x1=\"305\" y1=\"208\" x2=\"305\" y2=\"150\" stroke=\"#C8932A\" stroke-width=\"4\"><\/line>\n<polygon points=\"305,140 298,154 312,154\" fill=\"#C8932A\"><\/polygon>\n<line x1=\"200\" y1=\"103\" x2=\"142\" y2=\"103\" stroke=\"#C8932A\" stroke-width=\"4\"><\/line>\n<polygon points=\"132,103 146,96 146,110\" fill=\"#C8932A\"><\/polygon>\n<line x1=\"95\" y1=\"208\" x2=\"95\" y2=\"266\" stroke=\"#C8932A\" stroke-width=\"4\"><\/line>\n<polygon points=\"95,276 88,262 102,262\" fill=\"#C8932A\"><\/polygon>\n<line x1=\"200\" y1=\"313\" x2=\"258\" y2=\"313\" stroke=\"#C8932A\" stroke-width=\"4\"><\/line>\n<polygon points=\"268,313 254,306 254,320\" fill=\"#C8932A\"><\/polygon>\n<text x=\"318\" y=\"150\" font-family=\"Manrope, Arial, sans-serif\" font-size=\"15\" font-weight=\"700\" font-style=\"italic\" fill=\"#0A1628\">v<\/text>\n<text x=\"150\" y=\"92\" font-family=\"Manrope, Arial, sans-serif\" font-size=\"15\" font-weight=\"700\" font-style=\"italic\" fill=\"#0A1628\">v<\/text>\n<text x=\"70\" y=\"270\" font-family=\"Manrope, Arial, sans-serif\" font-size=\"15\" font-weight=\"700\" font-style=\"italic\" fill=\"#0A1628\">v<\/text>\n<text x=\"262\" y=\"335\" font-family=\"Manrope, Arial, sans-serif\" font-size=\"15\" font-weight=\"700\" font-style=\"italic\" fill=\"#0A1628\">v<\/text>\n<line x1=\"360\" y1=\"120\" x2=\"392\" y2=\"120\" stroke=\"#C8932A\" stroke-width=\"4\"><\/line>\n<polygon points=\"402,120 388,113 388,127\" fill=\"#C8932A\"><\/polygon>\n<text x=\"412\" y=\"125\" font-family=\"Manrope, Arial, sans-serif\" font-size=\"14\" fill=\"#1F2E47\">velocity vector (v)<\/text>\n<text x=\"360\" y=\"170\" font-family=\"Manrope, Arial, sans-serif\" font-size=\"14\" font-weight=\"700\" fill=\"#7A1F2B\">Same length<\/text>\n<text x=\"360\" y=\"190\" font-family=\"Manrope, Arial, sans-serif\" font-size=\"14\" fill=\"#1F2E47\">\u2192 the speed is constant<\/text>\n<text x=\"360\" y=\"232\" font-family=\"Manrope, Arial, sans-serif\" font-size=\"14\" font-weight=\"700\" fill=\"#7A1F2B\">Different directions<\/text>\n<text x=\"360\" y=\"252\" font-family=\"Manrope, Arial, sans-serif\" font-size=\"14\" fill=\"#1F2E47\">\u2192 the velocity changes<\/text>\n<text x=\"360\" y=\"300\" font-family=\"Manrope, Arial, sans-serif\" font-size=\"13\" fill=\"#142139\">Path direction: counter-clockwise<\/text>\n<\/svg>\n<p style=\"text-align:center;font-size:14px;color:#1F2E47;font-style:italic;margin-top:-0.5em;\">An object circling at a steady pace: every velocity arrow is the same length (speed is constant) but points a different way (velocity keeps changing) \u2014 which is why circular motion always involves acceleration.<\/p>\n<p>The diagram makes the point statically; the lab below lets you see it move. Set a speed, watch the velocity arrow keep its length while it rotates, and notice the displacement readout return to zero on every full lap as the distance just keeps climbing.<\/p>\n<div class=\"pf-sim-slot\"><div class=\"pf-sim-slot-header\"><span class=\"icon-dot\"><\/span><span class=\"label\">Velocity vs Speed Lab<\/span><\/div><div class=\"pf-sim-slot-body\"><style>.pf-sim-frame{width:100%;border:none;height:600px}@media(max-width:760px){.pf-sim-frame{height:1000px}}<\/style><iframe src=\"\/labs\/velocity-vs-speed.html\" class=\"pf-sim-frame\" loading=\"lazy\"><\/iframe><\/div><\/div>\n<h2>Real-World Examples of Speed and Velocity<\/h2>\n<p>The distinction stops being abstract the moment you look at how things actually move.<\/p>\n<p><strong>The running track.<\/strong> Sprint one full lap and your average speed is healthy, but your average velocity is zero \u2014 you finished exactly where you began, so your displacement is nil.<\/p>\n<p><strong>The daily commute.<\/strong> Drive to work and home again and you might clock 40 km on the odometer (real distance, real average speed), yet your net displacement for the day is zero. Velocity-wise, you went nowhere.<\/p>\n<p><strong>The roundabout.<\/strong> Holding 30 km\/h through the bend, your speed is constant while your velocity rotates continuously \u2014 the everyday face of acceleration without any change in pace.<\/p>\n<p><strong>The aircraft in wind.<\/strong> A plane&#8217;s airspeed might read a steady 250 knots, but a crosswind nudges its actual velocity sideways. Pilots plan around velocity \u2014 heading and speed together \u2014 because speed alone won&#8217;t get them to the right runway.<\/p>\n<h2>Average vs Instantaneous Speed and Velocity<\/h2>\n<p>So far we have mostly averaged over a whole journey. But motion rarely happens at one fixed rate, so physics needs two time-scales: the overall average and the snapshot.<\/p>\n<p><strong>Average velocity<\/strong> looks only at the endpoints \u2014 start here, finish there, divide the displacement by the time. The wandering path in between is ignored entirely. That is why average velocity can be exactly zero whenever you return to your starting point.<\/p>\n<svg viewBox=\"0 0 640 285\" role=\"img\" aria-label=\"A number line showing a 100 metre trip east then 100 metres west back to the start, giving 200 metres of total distance but zero net displacement, so average speed is 10 metres per second while average velocity is zero\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" style=\"width:100%;height:auto;max-width:640px;display:block;margin:1.5em auto;background:#F5F2EA;border-radius:6px;\">\n<text x=\"320\" y=\"30\" text-anchor=\"middle\" font-family=\"Manrope, Arial, sans-serif\" font-size=\"17\" font-weight=\"700\" fill=\"#7A1F2B\">Out and Back: Distance vs Displacement<\/text>\n<text x=\"294\" y=\"72\" text-anchor=\"middle\" font-family=\"Manrope, Arial, sans-serif\" font-size=\"13\" font-weight=\"700\" fill=\"#0A1628\">Leg 1: 100 m east, 10 s<\/text>\n<line x1=\"138\" y1=\"86\" x2=\"450\" y2=\"86\" stroke=\"#C8932A\" stroke-width=\"4\"><\/line>\n<polygon points=\"460,86 446,79 446,93\" fill=\"#C8932A\"><\/polygon>\n<line x1=\"110\" y1=\"126\" x2=\"540\" y2=\"126\" stroke=\"#0A1628\" stroke-width=\"2\"><\/line>\n<circle cx=\"130\" cy=\"126\" r=\"6\" fill=\"#142139\"><\/circle>\n<circle cx=\"460\" cy=\"126\" r=\"6\" fill=\"#142139\"><\/circle>\n<line x1=\"452\" y1=\"166\" x2=\"140\" y2=\"166\" stroke=\"#7A1F2B\" stroke-width=\"4\"><\/line>\n<polygon points=\"130,166 144,159 144,173\" fill=\"#7A1F2B\"><\/polygon>\n<text x=\"294\" y=\"186\" text-anchor=\"middle\" font-family=\"Manrope, Arial, sans-serif\" font-size=\"13\" font-weight=\"700\" fill=\"#7A1F2B\">Leg 2: 100 m west, 10 s<\/text>\n<text x=\"130\" y=\"210\" text-anchor=\"middle\" font-family=\"Manrope, Arial, sans-serif\" font-size=\"12.5\" fill=\"#1F2E47\">Start \/ Finish (0 m)<\/text>\n<text x=\"460\" y=\"210\" text-anchor=\"middle\" font-family=\"Manrope, Arial, sans-serif\" font-size=\"12.5\" fill=\"#1F2E47\">Turn-around (100 m E)<\/text>\n<text x=\"320\" y=\"246\" text-anchor=\"middle\" font-family=\"Manrope, Arial, sans-serif\" font-size=\"14\" font-weight=\"700\" fill=\"#0A1628\">Distance travelled = 200 m  \u2192  average speed = 10 m\/s<\/text>\n<text x=\"320\" y=\"272\" text-anchor=\"middle\" font-family=\"Manrope, Arial, sans-serif\" font-size=\"14\" font-weight=\"700\" fill=\"#7A1F2B\">Net displacement = 0 m  \u2192  average velocity = 0 m\/s<\/text>\n<\/svg>\n<p style=\"text-align:center;font-size:14px;color:#1F2E47;font-style:italic;margin-top:-0.5em;\">The same journey gives two very different answers: 200 m of ground covered (a real average speed) but no change in position (zero average velocity).<\/p>\n<p>Our headline example shows it cleanly. Drive 100 m east in 10 s, then 100 m west in 10 s: you covered 200 m of distance, so your average speed is a brisk 10 m\/s \u2014 but your displacement is zero, so your average velocity is 0 m\/s.<\/p>\n<p><strong>Instantaneous velocity<\/strong>, by contrast, is the value right now \u2014 at this exact tick of the clock. Its magnitude is the instantaneous speed.<\/p>\n<p>This is the difference between the speedometer and the trip computer. The speedometer shows your instantaneous speed; the trip computer&#8217;s &#8220;average speed since reset&#8221; is averaged over the whole drive. A common student slip is to assume average speed equals the magnitude of average velocity \u2014 true only for straight-line motion that never reverses.<\/p>\n<figure style=\"margin:32px auto;max-width:640px;text-align:center;\">\n  <img decoding=\"async\" src=\"https:\/\/physicsfundamentalsinfo.com\/blog\/wp-content\/uploads\/2026\/06\/Toyota_Corolla_2016_speedometer.jpg\"\n       alt=\"Car speedometer showing instantaneous speed in km\/h, a scalar with no direction\"\n       loading=\"lazy\"\n       style=\"width:100%;height:auto;border-radius:4px;\" \/>\n  <figcaption style=\"font-size:13px;color:#1F2E47;font-style:italic;margin-top:8px;\">A speedometer reads instantaneous speed only \u2014 magnitude with no direction. Add a compass and you would have velocity.<\/figcaption>\n<\/figure>\n<h2>Common Misconceptions About Speed and Velocity<\/h2>\n<p><strong>&#8220;Speed and velocity mean the same thing.&#8221;<\/strong> In casual talk, maybe. In physics, no \u2014 one is a scalar, the other a vector, and that lets velocity do something speed never can: average out to zero.<\/p>\n<p><strong>&#8220;Constant speed means constant velocity.&#8221;<\/strong> Only on a straight road. The instant the path curves, the direction changes, so the velocity changes \u2014 which is exactly why circular motion is accelerated motion.<\/p>\n<p><strong>&#8220;Average speed is just the size of average velocity.&#8221;<\/strong> Not in general. Because distance is always at least as large as the magnitude of displacement, average speed is always greater than or equal to the magnitude of average velocity; the two match only for straight-line motion without a U-turn.<\/p>\n<p><strong>&#8220;A speedometer reads velocity.&#8221;<\/strong> It reads speed \u2014 magnitude only. It has no idea whether you are heading north or south. Pair it with a compass and you would finally be measuring velocity.<\/p>\n<h2>How Speed and Velocity Relate to Acceleration, Displacement and Energy<\/h2>\n<p>Velocity sits at the centre of a web of other ideas, which is why getting it right pays off everywhere.<\/p>\n<p><strong>Acceleration<\/strong> is defined as the rate of change of velocity \u2014 so any change in speed or direction is an acceleration. That link runs straight into <a href=\"https:\/\/physicsfundamentalsinfo.com\/blog\/mechanics\/newtons-second-law\/\">Newton&#8217;s second law<\/a>, which says the net force needed equals mass times that acceleration.<\/p>\n<p>It also explains <a href=\"https:\/\/physicsfundamentalsinfo.com\/blog\/mechanics\/newtons-laws-of-motion\/\">Newton&#8217;s first law<\/a>: with no net force, an object keeps a constant velocity \u2014 not just a constant speed, but an unchanging direction too.<\/p>\n<p>Speed, meanwhile, is what powers <a href=\"https:\/\/physicsfundamentalsinfo.com\/blog\/mechanics\/what-is-energy-in-physics\/\">kinetic energy<\/a>, which depends on the square of the speed (\u00bdmv\u00b2). Two cars moving at the same speed in opposite directions have identical kinetic energy, because energy doesn&#8217;t care about direction \u2014 only magnitude.<\/p>\n<p>And whenever something slows down, a force is changing its velocity. Often that force is <a href=\"https:\/\/physicsfundamentalsinfo.com\/blog\/mechanics\/what-is-friction\/\">friction<\/a>, quietly bleeding speed away until the motion stops.<\/p>\n<h2>Worked Problems<\/h2>\n<div class=\"pf-problem\"><div class=\"pf-problem-num\">Problem 1<\/div><div class=\"pf-problem-question\">A sprinter runs 100 m due north along a straight track in 12.5 s. Find (a) her average speed and (b) her average velocity.<\/div><details><summary>Show Solution<\/summary><div class=\"pf-problem-solution\">\n<strong>Solution:<\/strong><br>\nStep 1: The path is a straight line with no reversal, so distance = magnitude of displacement = 100 m, and the time is t = 12.5 s.<br>\nStep 2 (average speed): average speed = distance \/ time = 100 m \/ 12.5 s.<br>\nStep 3: average speed = 8.0 m\/s.<br>\nStep 4 (average velocity): average velocity = displacement \/ time = 100 m \/ 12.5 s = 8.0 m\/s, directed due north.<br>\n<strong>Answer: average speed = 8.0 m\/s; average velocity = 8.0 m\/s due north \u2014 equal in size because the motion is a straight line.<\/strong>\n<\/div><\/details><\/div>\n<div class=\"pf-problem\"><div class=\"pf-problem-num\">Problem 2<\/div><div class=\"pf-problem-question\">A car travels 100 m east in 10 s, then 100 m west in 10 s, returning to its starting point. Find (a) the average speed and (b) the average velocity for the whole trip.<\/div><details><summary>Show Solution<\/summary><div class=\"pf-problem-solution\">\n<strong>Solution:<\/strong><br>\nStep 1: Total distance = 100 m + 100 m = 200 m. Total time = 10 s + 10 s = 20 s.<br>\nStep 2 (average speed): average speed = total distance \/ total time = 200 m \/ 20 s = 10 m\/s.<br>\nStep 3 (displacement): the car ends where it began, so the net displacement \u0394x = 0 m.<br>\nStep 4 (average velocity): average velocity = \u0394x \/ \u0394t = 0 m \/ 20 s = 0 m\/s.<br>\n<strong>Answer: average speed = 10 m\/s; average velocity = 0 m\/s. Same journey, two very different numbers.<\/strong>\n<\/div><\/details><\/div>\n<div class=\"pf-problem\"><div class=\"pf-problem-num\">Problem 3<\/div><div class=\"pf-problem-question\">A runner completes one full lap of a 400 m track in 80 s, finishing at the starting line. Find (a) the average speed and (b) the average velocity.<\/div><details><summary>Show Solution<\/summary><div class=\"pf-problem-solution\">\n<strong>Solution:<\/strong><br>\nStep 1: One lap means the distance travelled = 400 m over a time t = 80 s.<br>\nStep 2 (average speed): average speed = distance \/ time = 400 m \/ 80 s = 5.0 m\/s.<br>\nStep 3 (displacement): start and finish are the same point, so displacement = 0 m.<br>\nStep 4 (average velocity): average velocity = 0 m \/ 80 s = 0 m\/s.<br>\n<strong>Answer: average speed = 5.0 m\/s; average velocity = 0 m\/s.<\/strong>\n<\/div><\/details><\/div>\n<div class=\"pf-problem\"><div class=\"pf-problem-num\">Problem 4<\/div><div class=\"pf-problem-question\">A delivery van drives 3.0 km due east, then 4.0 km due north, taking 0.20 h in total. Find (a) the total distance, (b) the magnitude of the displacement, (c) the average speed and (d) the magnitude of the average velocity.<\/div><details><summary>Show Solution<\/summary><div class=\"pf-problem-solution\">\n<strong>Solution:<\/strong><br>\nStep 1 (distance): total distance = 3.0 km + 4.0 km = 7.0 km.<br>\nStep 2 (displacement): the two legs are at right angles, so use Pythagoras \u2014 magnitude of displacement = \u221a(3.0\u00b2 + 4.0\u00b2) = \u221a(9.0 + 16.0) = \u221a25.0 = 5.0 km.<br>\nStep 3 (average speed): average speed = total distance \/ time = 7.0 km \/ 0.20 h = 35 km\/h.<br>\nStep 4 (average velocity): magnitude = displacement \/ time = 5.0 km \/ 0.20 h = 25 km\/h, directed at tan\u207b\u00b9(4.0 \/ 3.0) \u2248 53\u00b0 north of east.<br>\n<strong>Answer: distance = 7.0 km; displacement = 5.0 km; average speed = 35 km\/h; average velocity = 25 km\/h at about 53\u00b0 north of east.<\/strong>\n<\/div><\/details><\/div>\n<div class=\"pf-problem\"><div class=\"pf-problem-num\">Problem 5<\/div><div class=\"pf-problem-question\">An object moves in a circle of radius 2.0 m at a constant speed of 4.0 m\/s. (a) Is its velocity constant? (b) What is its speed after half a revolution? (c) How long does one full revolution take?<\/div><details><summary>Show Solution<\/summary><div class=\"pf-problem-solution\">\n<strong>Solution:<\/strong><br>\nStep 1 (a): No. The speed stays the same, but the direction of motion changes continuously, so the velocity vector is always changing \u2014 the object is accelerating.<br>\nStep 2 (b): Speed is a scalar and is held constant here, so after half a revolution the speed is still 4.0 m\/s \u2014 only the direction has flipped.<br>\nStep 3 (c): one revolution covers the circumference, C = 2\u03c0r = 2\u03c0(2.0 m) = 12.57 m.<br>\nStep 4: time for one revolution T = C \/ speed = 12.57 m \/ 4.0 m\/s = 3.14 s.<br>\n<strong>Answer: (a) no \u2014 velocity is not constant; (b) 4.0 m\/s; (c) T \u2248 3.1 s.<\/strong>\n<\/div><\/details><\/div>\n<div class=\"pf-problem\"><div class=\"pf-problem-num\">Problem 6<\/div><div class=\"pf-problem-question\">A particle moves along the x-axis with its position given by x = t\u00b2 (x in metres, t in seconds). Find (a) its average velocity from t = 0 to t = 2.0 s, (b) its instantaneous velocity at t = 2.0 s, and (c) why the two values differ.<\/div><details><summary>Show Solution<\/summary><div class=\"pf-problem-solution\">\n<strong>Solution:<\/strong><br>\nStep 1 (positions): x(0) = 0\u00b2 = 0 m and x(2.0) = (2.0)\u00b2 = 4.0 m, so displacement \u0394x = 4.0 \u2212 0 = 4.0 m.<br>\nStep 2 (a \u2014 average velocity): average velocity = \u0394x \/ \u0394t = 4.0 m \/ 2.0 s = 2.0 m\/s.<br>\nStep 3 (b \u2014 instantaneous velocity): differentiate, v = dx\/dt = 2t; at t = 2.0 s, v = 2(2.0) = 4.0 m\/s.<br>\nStep 4 (c): the particle speeds up the whole time (v = 2t grows with t), so its rate at the final instant (4.0 m\/s) is larger than its average over the interval (2.0 m\/s).<br>\n<strong>Answer: (a) 2.0 m\/s; (b) 4.0 m\/s; (c) the motion is accelerating, so the instantaneous value at the end exceeds the interval average.<\/strong>\n<\/div><\/details><\/div>\n<h2>Frequently Asked Questions<\/h2>\n<details class=\"pf-faq-item\"><summary>Is velocity the same as speed?<\/summary><div class=\"pf-faq-item-answer\">\nNo. Speed is a scalar that records only how fast something moves, while velocity is a vector that records how fast and in which direction it moves. Speed is actually the magnitude of velocity, so every velocity contains a speed \u2014 but a speed on its own has had its direction removed. That is why two objects can share a speed yet have different, even opposite, velocities.\n<\/div><\/details>\n<details class=\"pf-faq-item\"><summary>Can speed be constant while velocity changes?<\/summary><div class=\"pf-faq-item-answer\">\nYes. Any object moving along a curved path at a steady pace has a constant speed but a continuously changing velocity, because its direction keeps changing. A car rounding a bend at 30 km\/h and a satellite circling Earth are everyday and cosmic examples. Whenever velocity changes \u2014 even if only its direction does \u2014 the object is accelerating.\n<\/div><\/details>\n<details class=\"pf-faq-item\"><summary>Which one is a vector, speed or velocity?<\/summary><div class=\"pf-faq-item-answer\">\nVelocity is the vector; speed is the scalar. A vector has both magnitude and direction, so velocity tells you how fast and which way (for example, 20 m\/s east). A scalar has magnitude only, so speed tells you just how fast (20 m\/s). In writing, velocity is often shown in bold or with a small arrow above the symbol to flag that it is a vector.\n<\/div><\/details>\n<details class=\"pf-faq-item\"><summary>Can average velocity be zero?<\/summary><div class=\"pf-faq-item-answer\">\nYes, whenever an object finishes exactly where it started. Average velocity equals displacement divided by time, and displacement is the straight-line change in position from start to finish. If you return to your starting point \u2014 a full lap, a round-trip commute \u2014 that displacement is zero, so the average velocity is zero, even though your average speed and the distance you covered are not.\n<\/div><\/details>\n<details class=\"pf-faq-item\"><summary>What is instantaneous velocity?<\/summary><div class=\"pf-faq-item-answer\">\nInstantaneous velocity is an object&#8217;s velocity at a single moment in time, rather than averaged over a journey. Mathematically it is the limit of displacement divided by time as the time interval shrinks toward zero \u2014 the derivative of position with respect to time. Its magnitude is the instantaneous speed, which is the value a speedometer displays at any given instant.\n<\/div><\/details>\n<details class=\"pf-faq-item\"><summary>Does a speedometer show speed or velocity?<\/summary><div class=\"pf-faq-item-answer\">\nA speedometer shows instantaneous speed only \u2014 a magnitude with no direction attached. It reads 60 km\/h whether you are driving north, south, or round in circles, because it cannot sense which way you point. To turn that reading into a velocity you would need to add direction, for example from a compass or a GPS heading.\n<\/div><\/details>\n<details class=\"pf-faq-item\"><summary>Do speed and velocity have the same units?<\/summary><div class=\"pf-faq-item-answer\">\nYes. Both are measured in metres per second (m\/s) in SI units, or in everyday units such as kilometres per hour (km\/h) or miles per hour (mph). The units never reveal which quantity you are dealing with \u2014 what distinguishes them is that velocity also specifies a direction, while speed does not.\n<\/div><\/details>\n\n\n\n\n<p class=\"wp-block-paragraph\"><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Speed is a scalar and velocity is a vector \u2014 that one difference is why average velocity can be zero on a round trip while you still cover real distance. Here&#8217;s the full breakdown with examples, worked problems and an interactive demo.<\/p>\n","protected":false},"author":1,"featured_media":174,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[7],"tags":[52,43,53,50,51,49],"class_list":["post-173","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-kinematics","tag-displacement","tag-kinematics","tag-motion","tag-speed","tag-vectors-and-scalars","tag-velocity"],"_links":{"self":[{"href":"https:\/\/physicsfundamentalsinfo.com\/blog\/wp-json\/wp\/v2\/posts\/173","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/physicsfundamentalsinfo.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/physicsfundamentalsinfo.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/physicsfundamentalsinfo.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/physicsfundamentalsinfo.com\/blog\/wp-json\/wp\/v2\/comments?post=173"}],"version-history":[{"count":2,"href":"https:\/\/physicsfundamentalsinfo.com\/blog\/wp-json\/wp\/v2\/posts\/173\/revisions"}],"predecessor-version":[{"id":177,"href":"https:\/\/physicsfundamentalsinfo.com\/blog\/wp-json\/wp\/v2\/posts\/173\/revisions\/177"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/physicsfundamentalsinfo.com\/blog\/wp-json\/wp\/v2\/media\/174"}],"wp:attachment":[{"href":"https:\/\/physicsfundamentalsinfo.com\/blog\/wp-json\/wp\/v2\/media?parent=173"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/physicsfundamentalsinfo.com\/blog\/wp-json\/wp\/v2\/categories?post=173"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/physicsfundamentalsinfo.com\/blog\/wp-json\/wp\/v2\/tags?post=173"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}