Motion in a straight line: x, v and a on one time axis

Year 12 Mathematics Advanced · metres and seconds · v = dx/dt, a = dv/dt · displacement is signed, distance is not
Position x(t)

Particle, then x, v, a against t

x(t) v(t) a(t)
Drag the cursor through a moment when v = 0. The particle stops and turns; x reaches a peak or a trough.
0 s

Arrow keys move the cursor by 0.05 s.

x(t) position 0
v(t) velocity 0
a(t) acceleration 0

Interval tool. Choose t1 and t2, predict, then reveal.

0 s
3 s

Predict, then reveal

On this interval, is the distance travelled equal to the size of the displacement, or greater?

Commit first. The numbers on the right stay hidden until you do.

Displacement versus distance on [t1, t2]

displacement x(t2) − x(t1) ?
distance ∫ |v| dt ?
rest times inside the interval ?

Split the interval at every rest time and add the sizes of the pieces.