Question

A body starts from rest and acquires a velocity v in time t. the work done on the body in time t will be proportional to:

Answer 1

Since,

V = 0 + at (by formula)

or a = V/T

So, at any time ‘t’ the velocity is,

v = 0 + at

or v = (V/T)t

Therefore, KE of the body after time t is,

KE = ½ (mv2)

or KE = ½ m[(V/T)t]2

We know, work done is equal to gain in KE

So, Work done = ½ m[(V/T)t]2

Thus, work done is directly proportional to [(V/T)t]2.

Answer 2

Since,

V = 0 + at (by formula)

or a = V/T

So, at any time ‘t’ the velocity is,

v = 0 + at

or v = (V/T)t

Therefore, KE of the body after time t is,

KE = ½ (mv2)

or KE = ½ m[(V/T)t]2

We know, work done is equal to gain in KE

So, Work done = ½ m[(V/T)t]2

Thus, work done is directly proportional to [(V/T)t]2.