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

In summary, it is not possible for a body to have zero velocity and non-zero acceleration at the same time. However, a body can have an instantaneous zero velocity and still have a non-zero acceleration, as seen in the example of a ball thrown up in the air. The acceleration of the ball is constant, but its velocity is constantly changing. Therefore, it is incorrect to assume that a body cannot have a constant acceleration and a time-varying velocity.
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Mitchtwitchita
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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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  • #2


Mitchtwitchita said:
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.
 
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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?
 
  • #4


Mitchtwitchita said:
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.)
 
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  • #5


Mitchtwitchita said:
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?

Perhaps I have missunderstood your question, but I think that a body traveling with a constant acceleration is not only able to have a time-varying velovity, it absolutely must have one. Perhaps you meant that a body under constant acceleration is unable to have a velovity that is constant over time? I would agree with that (form an inertial reference frame, of course). An accelerating body may have an "instantaeous zero velocity," as Zz said, but that velocity cannot remain zero over time.
 

FAQ: Possible for a body to have zero velocity and non-zero acceleration

Is it possible for a body to have zero velocity and non-zero acceleration at the same time?

Yes, it is possible for a body to have zero velocity and non-zero acceleration. This happens when the body is changing direction but not its speed. This is known as centripetal acceleration.

Can a body have zero velocity and non-zero acceleration in a straight line?

No, a body cannot have zero velocity and non-zero acceleration in a straight line. In a straight line, the direction of motion and acceleration are the same, so if the velocity is zero, the acceleration must also be zero.

What is the difference between zero velocity and zero acceleration?

Zero velocity means that the body is not moving at all, while zero acceleration means that the body is either at rest or moving at a constant speed. Velocity is a measure of both speed and direction, while acceleration is a measure of how the velocity is changing.

Can a body have zero velocity and non-zero acceleration at different points in time?

Yes, a body can have zero velocity and non-zero acceleration at different points in time. This can happen when the body is changing its velocity, for example, when it is slowing down or speeding up.

How does zero velocity and non-zero acceleration affect the motion of a body?

When a body has zero velocity and non-zero acceleration, it means that the body is either changing direction or changing speed. This can result in a curved or non-linear motion, depending on the direction and magnitude of the acceleration.

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