Jerk in Physics: the Displacement SUVAT Cannot See

SUVAT needs the acceleration to be constant. Let it ramp instead — at a steady jerk, j = da/dt — and the velocity–time graph stops being a straight line and becomes a parabola. The dashed line is the velocity SUVAT assumes; the solid curve is the truth; and the shaded band between them is the displacement SUVAT misses, exactly 1/6 j t^3. Start from rest with no acceleration and SUVAT predicts the lift never moves at all. The three lift jerks are reported passenger ratings, not a motion profile — holding 6 m/s3 for a full 2 s reaches 12 m/s2 and 12 m/s, and no real lift does that.

Velocity at t4.000 m/s

Acceleration at t4.000 m/s2

Mean acceleration2.000 m/s2

Trapezium estimate4.000 m

Simpson, the area rule2.667 m

SUVAT with the final a8.000 m

The u t term0.000 m

The 1/2 a0 t^2 term0.000 m

The 1/6 j t^3 term2.667 m

The bandThe shaded band between the dashed line and the solid curve is the displacement SUVAT misses: the solid curve runs above the dashed line the whole way, so the straight-line answer is short by 2.667 m.

Displacement s = u t + 1/2 a0 t^2 + 1/6 j t^3

2.667 m

What SUVAT says s = u t + 1/2 a0 t^2

0.000 m

The term SUVAT drops 1/6 j t^3

2.667 m

Which term is biggest

Jerk dominates

Initial velocity0.000 m/s

Initial acceleration0.000 m/s2

Jerk2.00 m/s3

Elapsed time2.00 s

Simpson always agrees with the answer because the velocity curve is a parabola and Simpson's rule is exact for cubics — that is algebra, not a check. So is the fact that the term SUVAT drops equals the answer minus the SUVAT figure. Constant jerk is itself an idealisation: it is the next term, not the last one. ISO 8100-34 does not set a jerk limit — it says how to measure ride quality.