A body of mass m accelerates uniformly from rest to velocity `upsilon_1` in time `t_1`.The instaantaneous power delivered to the body as a function of time t is

Options

A. `(m upsilon_1 t)/(t_1)`
B. `(m upsilon_1^2 t)/(t_1^2)`
C. `(m upsilon_1^2 t^2)/(t_1^2)`
D. `(m upsilon_1 t^2)/(t_1)`

Answer

B

Explanation

Power delivered in time `t_1` is `P_1 = F. v_1 = m a. v_1` .
Now, acceleration vector is `a = (v_1)/(t_1)`. Therefore `P_1 = (m upsilon_1 . upsilon_1)/(t_1) = (m upsilon_1^2)/(t_1)`
`therefore` Power delivered per unit time = `(P_1)/(t_1)`, Power delivered per unit time `t = (P_1)/(t_1) xx t = (m upsilon_1^2 t)/(t_1^2)`
Hence the correct choice is (B). Notice that choices (A),(C) and (D) do not have the dimensions of power.