Register to reply

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

by Mitchtwitchita
Tags: acceleration, body, nonzero, velocity
Share this thread:
Mitchtwitchita
#1
Sep21-08, 06:29 PM
P: 190
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?
Phys.Org News Partner Physics news on Phys.org
Physicists unlock nature of high-temperature superconductivity
Serial time-encoded amplified microscopy for ultrafast imaging based on multi-wavelength laser
Measuring the smallest magnets: Physicists measured magnetic interactions between single electrons
ZapperZ
#2
Sep21-08, 08:16 PM
Emeritus
Sci Advisor
PF Gold
ZapperZ's Avatar
P: 29,239
Quote Quote by Mitchtwitchita View Post
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.
Mitchtwitchita
#3
Sep21-08, 09:09 PM
P: 190
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?

atyy
#4
Sep21-08, 09:46 PM
Sci Advisor
P: 8,373
Possible for a body to have zero velocity and non-zero acceleration

Quote Quote by Mitchtwitchita View Post
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.)
LURCH
#5
Sep22-08, 10:58 AM
Sci Advisor
P: 2,510
Quote Quote by Mitchtwitchita View Post
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.


Register to reply

Related Discussions
Vector v = a i +bxj Classical Physics 9
Kinematics Introductory Physics Homework 5
Kinematic physics questions General Physics 0
Kinematics Introductory Physics Homework 3
Kinematics Introductory Physics Homework 4