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  4. A body is initially at rest. It undergoes one dimensional motion with constant acceleration. The power delivered to it at time t is proportional to

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Q. A body is initially at rest. It undergoes one dimensional motion with constant acceleration. The power delivered to it at time $t$ is proportional to

BHUBHU 2006Work, Energy and Power

Solution:

Using $ v = u + at $
$ \therefore v = at\quad\left(\because u = 0\right) $
As power, $ P = F \times v $
$ \therefore P = \left(ma\right) \times at = ma^{2}t $
As m and a are constants,
$ \therefore P \propto t $