possible for a body to have zero velocity and non-zero acceleration

by Mitchtwitchita
Tags: acceleration, body, nonzero, velocity
 P: 191 Is it possible for a body to have zero velocity and non-zero acceleration. I would have to say no because acceleration is the time rate of change of velocity. So, if velocity isn't changing, how can there be an acceleration. Is this answer accurate?
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P: 27,640
 Quote by Mitchtwitchita Is it possible for a body to have zero velocity and non-zero acceleration. I would have to say no because acceleration is the time rate of change of velocity. So, if velocity isn't changing, how can there be an acceleration. Is this answer accurate?
You're forgetting that a body can have an instantaneous zero velocity, and yet, it's velocity is also changing. Throw a ball up in the air. At the highest peak, it's velocity has a zero velocity for an instant. Yet, all through the motion, it still has an acceleration that is non-zero, which is g.

Zz.
 P: 191 Gravity!!! Then I guess, I would have been wrong. So, I would have to say now that a body is unable to travel with a constant acceleration and a time-varying velocity. Would you say that this is a correct assumption?
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possible for a body to have zero velocity and non-zero acceleration

 Quote by Mitchtwitchita Gravity!!! Then I guess, I would have been wrong. So, I would have to say now that a body is unable to travel with a constant acceleration and a time-varying velocity. Would you say that this is a correct assumption?
No. Let's take Zz's example of a ball thrown up in the air. We pretend the earth is so large that it doesn't move, and only the ball does. The ball moves only a short distance, so we approximate the gravitational force to be constant over the ball's trajectory.

Force of gravity between the ball and earth = mg,
where m is the mass of the ball
where g is a constant, which represents the "effect of the gravitational mass of the earth".

Newton's 2nd law, F=ma,
where F is the total force on the ball
where m is again the mass of the ball
where a is the acceleration of the ball in response to F.

Since gravity is the only force on the ball, we combine the force of gravity and Newton's 2nd law as follows: mg=ma.
Hence a=g.

So the acceleration of the ball is constant in magnitude and direction. When you throw the ball upwards, a is downwards and opposite to the velocity, so the ball "decelerates". At the top of the trajectory, the ball has instantaneous 0 velocity. Then it moves downwards, a is still downwards but now in the same direction as the velocity, and the ball "accelerates". (Sorry I used "accelerate" in two slightly different ways here, hence the bolding for the first technically correct use, and the quotes over the second colloquial use.)