# Homework Help: Change in direction under constant acceleration?

1. Jun 21, 2014

1. The problem statement, all variables and given/known data

Can an object with constant acceleration reverse its direction of travel? Can it reverse its direction twice?

2. Relevant equations

Basic kinematics.

3. The attempt at a solution

First I thought that it is not possible to reverse direction because if direction changes acceleration would change. But later I thought about free fall and realized indeed it's possible to reverse direction even under constant acceleration if it's acting in opposite direction of velocity.

But I don't think a particle can reverse direction twice if it's under constant acceleration.

Am I correct?

[These are perhaps too basic questions to post. But I don't have any other way to check myself. I appreciate your help very much.]

2. Jun 21, 2014

### D H

Staff Emeritus
What do you mean by "constant acceleration": constant in magnitude, or constant in direction and magnitude? There's a big difference.

3. Jun 21, 2014

I mean constant in magnitude and direction.

4. Jun 21, 2014

### Orodruin

Staff Emeritus
If acceleration is constant, can you find an expression for the velocity? How can you relate this expression to your question?

5. Jun 21, 2014

### Satvik Pandey

Yes in case of uniform circular motion,acceleration is constant (as it is uniform circular motion so acceleration is constant in terms of magnitude and its direction is always towards the center) and the direction of object changes at every point.

Last edited: Jun 21, 2014
6. Jun 21, 2014

### Orodruin

Staff Emeritus
Just as the velocity changes during the circular motion, so does the direction to the center (both rotate with the same angular frequency). Thus, acceleration is not constant in this case, it is only constant in magnitude.

7. Jun 21, 2014

Direction towards a center does not mean it is having the same direction. See the example below:

The two arrows are pointing towards the same point. However, the direction of two vectors are obviously opposite.

This is what's happening in circular motion too. The direction of the acceleration vector is always changing.

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8. Jun 21, 2014

Yes. v = v0 + at
Now if I suppose that the particle is moving in positive direction then the particle will change its direction if v becomes negative, which is possible if an acceleration in negative direction is present for enough time.
Now if we want to change the particle's direction for the second time, certainly we will have to change the direction of acceleration and so acceleration won't remain constant.

So I can say - A particle under constant acceleration (in both magnitude and direction) may change its (the particle's) direction but for only once if the acceleration is to remain constant.

Are my explanations correct ??

9. Jun 21, 2014

### Orodruin

Staff Emeritus
It would become slightly more complicated if you go to more than one dimension (the acceleration will have to be proportional to the velocity so that you basically reduce to the 1D case), but the essence is there. It boils down to the velocity being a linear function of time. The direction is reversed when v=0, which happens exactly once between $t = -\infty$ and $t=\infty$.

10. Jun 22, 2014

### Satvik Pandey

Thank you for such a nice explanation.I was wrong,acceleration is not constant in this case.