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 v₀.
• Switching direction abruptly, the marble rebounds with speed v₀.
• Again moving under the influence of gravity only, the marble decelerates at 9.81 m s^-2, returning to rest at the starting position.

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

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• 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 –v₀ to v₀ in a negligibly short duration of time. This abrupt change in velocity is a very large acceleration. (Think , where Δt is the very short duration of contact.) This explains the spikes on the a-t graphs.

• 02 Kinematics