A car starts from the origin at t = 0. At some later time, is it possible for the car's velocity to be positive but its displacement from the origin to be zero? Explain and give an example.

  yes

Explanation:

In a simple case, the car starts with negative velocity, then stops and starts again with positive velocity. At some point, it will be back at the origin with positive velocity.

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All that is required to meet the described condition is that the area under the velocity (vs. time) curve be zero at a point where the velocity curve is greater than zero. This will require the velocity be negative at some point prior to the time of interest.

potential energy is directly proportional to height.

more height = more potential energy.

greatest increase in height = greatest increase in potential energy

where are the points with the greatest increase in height ?

has to be c-e or d-e .