How can there be acceleration but no velocity at instant of maximum height when object projected upwards?When we project an object vertically upwards its velocity at maximum height consider to be zero but still, it has acceleration due to gravity i.e 9.8 m / s 2 . But mathematically we know that acceleration is the first derivative of velocity with respect to time ( a = d v / d t ). So mathematically if velocity is zero there can not be any acceleration but this case contradict this equation. We can not even say that its direction is changing as the direction has no meaning without magnitude. So how this situation can be explained mathematically?

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How can there be acceleration but no velocity at instant of maximum height when object projected upwards?When we project an object vertically upwards its velocity at maximum height consider to be zero but still, it has acceleration due to gravity i.e   9.8      m          /              s      2      . But mathematically we know that acceleration is the first derivative of velocity with respect to time   (  a  =  d  v      /    d  t  ). So mathematically if velocity is zero there can not be any acceleration but this case contradict this equation. We can not even say that its direction is changing as the direction has no meaning without magnitude. So how this situation can be explained mathematically?

Pignatpmv · Accepted Answer

Acceleration is defined as            a      →        =            d                        v          →                            d      t      At maximum height             v      →       is zero but it doesn&#039;t means that             d                        v          →                            d      t        =  0 because at just the next moment i.e.   d  t the particle gains some velocity i.e.   d  v in downward direction.

Zackary Diaz · Accepted Answer

This can be a difficult concept at first. But notice the following facts:1. At the top of the trajectory, for an instant, the velocity is zero.2. An instant later, the velocity is non-zero. The particle is falling downward.That means, the velocity has changed from zero to non-zero. What is acceleration but a change in velocity? If there were no change in velocity (no acceleration), the velocity would remain zero --- the particle would just kinda float stationary in the air. That&#039;s clearly nonsense.Because the velocity doesn&#039;t stay at zero, then there must have been an acceleration.

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