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)?

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Answer 1 · 2018-03-14T14:29:37

Applying the equation, #v^2=u^2 +2as# (for constant acceleration #a#)

If the body started from rest,then,#u=0#,so total displacement, #s=v^2/(2a)# (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 #d x# amount of displacement is #dW =F*dx#

so, #dW =madx#

or, #int_0^WdW =maint_0^s dx#

so,#W=ma[x]_0^(v^2/(2a))# (as, #s=v^2/(2a)#)

so,#W=ma(v^2)/(2a)=1/2mv^2#

Proved