Question

A body of mass m accelerates uniformly from rest to $v_1$ in time $t_1$. The instantaneous power delivered to get body as a function of time t is:

• A. $\frac{m{v}_1{t}^2}{t_1}$
• B. $\frac{m{v}_2{t}^2}{t_1^2}$
• C. $\frac{m{v}_{1}t}{t_1}$
• D. None of the above

Answer 1

Answer: (A)

$\frac{m{v}_1{t}^2}{t_1}$

Let 'a be the constant acceleration equation of motion

$v=u+a{t}_1$

$v_1=0+a{t}_1$

$\Rightarrow a=\frac{v_1}{t_1}$

At any instant, the velocity ${}^{\prime }{v}^{\prime }$ of the body

$v=0+at$

$v=at$

$=\frac{v_1}{t_1}t$

$p=fv$

$=mav$

$\therefore P=m\left(\frac{v_1}{t_1}\right)\left(\frac{v_1}{t_1}t\right)$

$\therefore P=\frac{m{v}_1^2}{t_1^2}t$

Hence Answer is A.