Question

the displacement of a body is given by 2s=gt2 where g is constant .the velocity of the body at any time t is

Answer 1

s= 1/2*g*t^2
Now, this equation of motion for a body shows that the body is having a free fall because no intital velocity was given to the body.

From here,
Putting in
v^2 = 2gs
v^2 = 2g*1/2*g*t^2
v^2 = g^2*t^2

Therefore,
v= gt

Therefore velocity of the body at any time t equals
v = gt

Answer 2

HELLO THERE!

Equation relating S and t is:

2S = gt²

On differentiating both sides with respect to t, we get:

$2 \frac{dS}{dt} = g \frac{d(t^{2})}{dt} \\\\\implies 2v = g\times 2t \\\\\implies v = gt$

Since:

$\frac{dS}{dt} = v$

And, derivative of t² = 2t.

So, the relation between v and t is given by

v = gt

Since g is constant, put the value of t, you will get the value of velocity (v).

THANKS!