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You are watching: Can an object with constant acceleration reverse its direction
This inquiry is native the book Sears and Zemansky"s university altoalsimce.org.
My answer come the an initial part that the concern is: Yes, in case of free fall when things is thrown up.
What about the second part? deserve to it readjust its direction twice? i cannot think of any kind of situation wherein this can happen, so more than likely not. Is the possible?
A adjust in direction needs $dx/dt$ to be zero (i.e. A stationary point where the velocity is zero).
If $dv/dt$ is constant, climate if the is positive, that is possible for $v$ to it is in initially negative and then go through zero. Or if $dv/dt$ is an adverse it is possible for $v$ to be initially positive and also go v zero.
However, it is impossible for the velocity to be zero ~ above two different occasions uneven $dv/dt$ changes sign and also thus the acceleration changes with time. Therefore it is not feasible to readjust direction twice under uniform acceleration.
Your answer to the an initial part is correct.
As come the second part: You are on the right track. The is not feasible to change direction twice, given constant acceleration.
To to convince yourself, imagine any kind of general $v-t$ graph - it would be straight line in instance of constant acceleration. Change in direction coincides to $v$ going from positive to negative or evil versa. Currently a directly line graph will certainly not intersect the x-axis more than once. So there you have actually your answer.
The answer relies on how numerous dimensions you space working in and also your definition of acceleration as a vector quantity or a scalar quantity.
If you have 1 dimension, climate no, velocity will never go native one direction to the opposite direction and also then back to the an initial direction. In bespeak to adjust directions the acceleration needs to be directed opposite to velocity. When velocity transforms direction the acceleration will be in the same direction so that velocity will certainly not change direction.
If you have actually >1 dimension and define acceleration as a vector quantity, climate an acceleration directed in any direction no parallel or anti-parallel to the velocity will cause the direction come constantly change. For instance velocity North and also acceleration West will certainly cause an item to constantly readjust direction towards the West. But this walk not median that the thing will have the ability to reverse that direction twice.
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If you have actually >1 dimension and also define acceleration as a scalar quantity, consider constant centripetal acceleration. The velocity transforms directions constantly.