Question

A particle is projected on a horizontal
frictionless surface from a point A such that
the constant acceleration is always directed
towards A. If it is projected with an initial
velocity V and magnitude of acceleration is a,
find the time at after which the particle passes
through point A​

Answer 1

Answer:

$\frac{2V}{a}$

Explanation:

Since the acceleration is always directed towards A

Therefore the motion is linear motion

Using second equation of motion,

$s = ut+\frac{1}{2} at^{2}$

Here s is displacement which is 0, since particle returns to point A

Initial velocity in the direction of displacement u is V

acceleration in the direction of displacement is a but it'll be negative since it is pointed towards A

Therefore,

$0 = Vt-\frac{1}{2} at^{2}$

or, $t(V-\frac{1}{2} at)=0$

But t is not 0

Therefore, $t = \frac{2V}{a}$

Answer 2

Above answer is correct

I can confirm

Thanks for the points ;)