Is the acceleration under gravity constant in every case. Even when the velocity equal to zero because there velocity after some seconds even the velocity doesn't increase much.
Is the acceleration under gravity constant in every case. Even when the velocity equal to zero because there velocity after some seconds even the velocity doesn't increase much.
Thee can well be an instant when a body has zero velocity but is still having non-zero acceleration at that instant.
Take a pendulum at its extreme points. The velocity is zero but it is accelerating.
Or a ball thrown up. At its highest point, it is momentarily stationary (speed is zero) but it is still accelerating under gravity (which is why it then gets a downward speed and comes back to your hand).
So there can well be cases where the velocity is zero but at that time the acceleration is non-zero (with the caveat that obviously the non-zero acceleration will also result immediately in non-zero speed).
Let us see this in more detail via a mathematical example.
Let magnitude of velocity at time t be Vsin(nt) where V is a non-zero constant with units m/sec, n is a non-zero constant with units degrees/sec, and t is a variable (time in seconds).
By differentiating against time t, we get the acceleration at time t as nVCos(nt) with units of m/sec^2.
At nt = 0 degrees, 180 degrees and so on, magnitude of instantaneous velocity is zero.
However at these nt = 0 degrees, 180 degrees etc cases, instantaneous acceleration is non-zero!! (even though magnitude of instantaneous velocity is zero at that instant).
Thee can well be an instant when a body has zero velocity but is still having non-zero acceleration at that instant.
Take a pendulum at its extreme points. The velocity is zero but it is accelerating.
Or a ball thrown up. At its highest point, it is momentarily stationary (speed is zero) but it is still accelerating under gravity (which is why it then gets a downward speed and comes back to your hand).
So there can well be cases where the velocity is zero but at that time the acceleration is non-zero (with the caveat that obviously the non-zero acceleration will also result immediately in non-zero speed).
Let us see this in more detail via a mathematical example.
Let magnitude of velocity at time t be Vsin(nt) where V is a non-zero constant with units m/sec, n is a non-zero constant with units degrees/sec, and t is a variable (time in seconds).
By differentiating against time t, we get the acceleration at time t as nVCos(nt) with units of m/sec^2.
At nt = 0 degrees, 180 degrees and so on, magnitude of instantaneous velocity is zero.
However at these nt = 0 degrees, 180 degrees etc cases, instantaneous acceleration is non-zero!! (even though magnitude of instantaneous velocity is zero at that instant).
