Creating a picture of the concept and example being taught , visualizing the mechanism , and embedding the factor of how in every concept , that how it happened , followed by an internal satisfaction and mental clearance is called logic!
Yes , it is possible that an object has non-zero kinetic energy at maximum height , But how ?
Suppose you’ve thrown a body in an oblique path ( Parabolic Path ) , At maximum height , vertical component of velocity becomes zero , but horizontal component of velocity is still present there , Hence , No Doubt Kinetic Energy has been reduced at maximum height but it is still present in the less quantity , because most of the energy has been converted into the potential energy
It is definitely possible that , at the instant when velocity is zero , acceleration is non-zero
First of all , you should know that , acceleration is not rate of velocity , but it is rate of change in velocity !
Following are 3 cases in which velocity at that instant is zero but acceleration is non-zero :
1 – When we apply sudden brakes to the car moving with some initial velocity along positive x axis velocity becomes zero but acceleration is negative and non-zero
2 – In vertical upward motion when body is at highest point velocity is zero but acceleration is -g in the absence of air resistance.
3 – In SHM of simple pendulum for amplitudes less than 10 degrees , The bob at maximum extreme position has zero velocity , but maximum acceleration because displacement is maximum