# Sign of Acceleration of dropped tennis ball at the floor

## Homework Statement

You drop a tennis ball on a hard floor, and it bounces upward. If the x-axis is directed upward, what is the sign of the acceleration while the ball is in contact with the floor?

a=v/t

## The Attempt at a Solution

I thought that the acceleration when the ball hits the floor would be 0 because the ball's speed is 0 at that point in time, and because there was no acceleration at that point then there would be no sign for it. The correct answer is that the acceleration is positive. As a side note, I believe the ball does not have a direction when it is in contact with the ground (please correct me if I'm wrong).

## Answers and Replies

A ball can have 0 speed and a non-zero acceleration. In fact, it has to in order to go from a stopped position (floor) to a velocity that is not zero(upward)

A ball can have 0 speed and a non-zero acceleration. In fact, it has to in order to go from a stopped position (floor) to a velocity that is not zero(upward)
Okay, that makes sense. Thanks a lot!

CWatters
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And it does have a direction.

haruspex
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There is a small flaw in the question. From the instant the ball touches the floor, the acceleration will continue to be downwards until the point at which the compressive force in the ball matches the ball's weight. Similarly, after rebounding to the same point, the acceleration will again be downwards.

• Vibhor and CWatters
James R
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I thought that the acceleration when the ball hits the floor would be 0 because the ball's speed is 0 at that point in time, and because there was no acceleration at that point then there would be no sign for it. The correct answer is that the acceleration is positive. As a side note, I believe the ball does not have a direction when it is in contact with the ground (please correct me if I'm wrong).
Remember that acceleration is proportional to force (F=ma). So, if the ball has a net force on it then it must be accelerating.

When the ball is in contact with the ground it has two forces on it: the force of gravity pulling it down and the force of the floor pushing it upwards. To make the ball bounce upwards off the ground, the upwards force must be, on average, greater than the force of gravity. So, there is a net upwards force during the bounce, and therefore a net upwards acceleration.

A slight complication: the magnitude of the force on the ball due to the floor actually varies during the time the ball is in contact with the floor, but it is always directed upwards (it's a normal force).