Question

Can body have zero velocity and still be accelerating?

Answer 1

Yes, an object can have zero velocity and still be accelerating simultaneously.

When the object stops for a moment its velocity at that instant is zero, therefore no motion in either forward or backward direction.

However the acceleration is still acting on it.

Answer 2

$<b><i>$YES, An object can have zero velocity and still be accelerating.

If an object is considered which is moving in forward direction and when a force is acting on this object makes it accelerate in backward direction, then it can be noticed that the object continues to move forward for some time and stop momentarily. Then the object will try to move in backward direction.

Here, At the instant when the object stopped moving, it's velocity (at that instant) is zero.
So there will be no motion either in forward or backward direction but it is to be noted that the acceleration is still acting on it.
At that instant, the magnitude of the velocity in backward direction is equal to the magnitude of velocity in forward direction. But as the acceleration continues on it, the velocity in the backward direction increases in magnitude over time and object finally starts moving in backward direction.

The same can also be shown mathematically as follows :

We know,
Acceleration = Rate of change of velocity
$a = \frac{d}{dt}[v]$

Let Velocity of any object at a time 't' be denoted by v(t)= t -2 ----------[1]

Then the acceleration of the object
$a(t) = \frac{d}{dt}[v(t)]$

$= \frac{d}{dt}(t-2)$

$= \frac{d}{dt}(t) -\frac{d}{dt}(2)$

$= 1-0$

a(t) =1----------[2]

When t=2, Velocity of the object is given as
v(t)= 2-2 = 0
v(t) = 0

When t= 2, Acceleration of the object is given as
a(t)= 1

Clearly,
At t=2,
Velocity of an object v(t) is zero but the acceleration a(t) is still constant i.e., 1

This proves that an object can have zero velocity and still be accelerating.