How can we prove that the work done to accelerate a body from rest to a velocity, V is given by W=1/2(mV^2)?

1 Answer
Mar 14, 2018

Applying the equation, v2=u2+2as (for constant acceleration a)

If the body started from rest,then,u=0,so total displacement, s=v22a (where,v is the velocity after displacement s)

Now,if force F acted on it,then F=ma (m is its mass)

so,work done by force F in causing dx amount of displacement is dW=Fdx

so, dW=madx

or, W0dW=mas0dx

so,W=ma[x]v22a0 (as, s=v22a)

so,W=mav22a=12mv2

Proved