# Is it possible for an object to have zero velocity, but have a non-zero acceleration?

1. Sep 28, 2016

### Gopal Mailpalli

Can you list few examples.

2. Sep 28, 2016

### Staff: Mentor

Is this homework?

3. Sep 28, 2016

### Gopal Mailpalli

No dale, it isn't home work. While doing a problem (self-study), i came across this. So asked here.

4. Sep 28, 2016

### Staff: Mentor

Ok, you should still show some effort and thought about it on your own. How are velocity and acceleration defined?

5. Sep 28, 2016

### Gopal Mailpalli

The rate of change of velocity is acceleration.

6. Sep 28, 2016

### Staff: Mentor

And what is velocity?

7. Sep 28, 2016

### Gopal Mailpalli

Velocity is defined as the rate of change of position. Velocity is the first derivative of position with respect to time, where as acceleration is the second derivative of position.

8. Sep 28, 2016

### A.T.

And how are those points called where the 1st derivative is zero, but the 2nd isn't.

9. Sep 28, 2016

### Staff: Mentor

Perfect. So if, for example, your position is $x=-t^2+3t+5$, then what is your velocity and acceleration?

10. Sep 28, 2016

### Gopal Mailpalli

Velocity is -2t + 3 and acceleration is -2, with its respective units.

11. Sep 28, 2016

### Gopal Mailpalli

Pardon me, I didn't understand the question.

12. Sep 28, 2016

### Ibix

13. Sep 28, 2016

### Staff: Mentor

Correct. So is there any t for which v=0? What is the acceleration at that time?

Also, plot the position as a function of time. Do you notice anything special about the time you found above?

14. Sep 28, 2016

### mathman

Think of the motion of a pendulum.

15. Sep 30, 2016

### Gopal Mailpalli

Thank you, i understood that at extreme positions, the velocity remains zero but acceleration is non-zero (changes its sign)

16. Sep 30, 2016

### Gopal Mailpalli

For t = 3/2, the velocity is zero. Based on the graph, the position of the object is constant w.r.t time. How would one determine the acceleration then?

17. Sep 30, 2016

### Staff: Mentor

Well done!

You already found the acceleration above, a=-2, regardless of time. Visually, a negative acceleration gives a position graph which is concave down, and a positive acceleration gives a position graph which is concave up. Since this graph is concave down everywhere you can immediately tell that the acceleration is negative everywhere.

18. Sep 30, 2016

### A.T.

Velocity doesn't remain zero, because acceleration is not zero. Velocity is instantaneously zero.

The velocity changes its sign, not the acceleration.