Question

work done in time T on a body of mass M which is accelerated from rest to a speed V in time T1 as a function of time T is given by ​

Answer 1

W = F × s

and

F = m × a

so

W = m × a × s

"The body is accelerated from 0 to v in time t1"

so

v = 0 + a × t1

a = v / t1

The distance traveled in a certain time t is W = m × (v / t1) × ( (v × t²) / (2 × t1) )

Rearranging the equation,

W = (m × v² × t²) / (2 × t1²)

Or, W = ( m × v² / 2 ) × ( t / t1 )²