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This inquiry is from the book Sears and Zemansky\"s university starrkingschool.net.
My answer come the an initial part that the question is: Yes, in situation of cost-free fall when things is thrown up.
What around the second part? can it readjust its direction twice? ns cannot think of any situation where this deserve to happen, so more than likely not. Is that possible?
A change in direction calls for $dx/dt$ to it is in zero (i.e. A stationary allude where the velocity is zero).
If $dv/dt$ is constant, then if that is positive, that is feasible for $v$ to be initially negative and climate go with zero. Or if $dv/dt$ is an adverse it is feasible for $v$ come be at first positive and go with zero.
However, it is impossible because that the velocity to it is in zero top top two separate occasions uneven $dv/dt$ transforms sign and also thus the acceleration changes with time. Therefore it is not feasible to adjust direction twice under uniform acceleration.
Your answer to the first part is correct.
As to the second part: You space on the right track. It is not feasible to change direction twice, given constant acceleration.
To to convince yourself, imagine any kind of general $v-t$ graph - it would certainly be directly line in case of consistent acceleration. Change in direction coincides to $v$ walk from confident to an unfavorable or angry versa. Now a right line graph will certainly not intersect the x-axis an ext than once. So there you have actually your answer.
The answer counts on how numerous dimensions you are working in and your an interpretation of acceleration together a vector quantity or a scalar quantity.
If you have 1 dimension, climate no, velocity will never ever go native one direction come the the opposite direction and then earlier to the an initial direction. In bespeak to readjust directions the acceleration has to be command opposite to velocity. Once velocity alters direction the acceleration will certainly be in the exact same direction so that velocity will not adjust direction.
If you have >1 dimension and also define acceleration as a vector quantity, then an acceleration command in any kind of direction not parallel or anti-parallel to the velocity will reason the direction come constantly change. For instance velocity North and acceleration West will cause things to constantly readjust direction towards the West. However this walk not typical that the object will have the ability to reverse that is direction twice.
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If you have >1 dimension and define acceleration as a scalar quantity, consider constant centripetal acceleration. The velocity alters directions constantly.