Scenario

A marble, dropped from rest at height *H* above the floor, is allowed to bounce off the floor two times. The collision with the floor is completely elastic and negligibly short. Sketch the marbles’s *v-t*, *s-t* and *a-t* graphs.

Solution

- (xmtutor)
- (xmdemo)
- Since this motion involves both upward and downward velocity, the more intuitive “
**upward is positive**” sign convention is adopted.

- The marble starts from rest, accelerates at a constant rate of 9.81 m s
^{-2} before colliding with the floor at the maximum speed of *v*_{0}.
- Switching direction abruptly, the marble rebounds with speed
*v*_{0}.
- Again moving under the influence of gravity only, the marble decelerates at 9.81 m s
^{-2}, returning to rest at the starting position.

–

- The
*s-t* graph consists of quadratic curve segments between bounces.

–

- The marble has a constant downward acceleration of
*g* except when it is in contact with the floor.
- During each bounce, the velocity changes from –
*v*_{0} to *v*_{0} in a negligibly short duration of time. This abrupt change in velocity is a very large acceleration. (Think , where Δ*t* is the very short duration of contact.) This explains the spikes on the *a-t *graphs.

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