Question

A body of mass $m$ accelerates uniformly from rest to velocity $v_1$ in time interval $T_1$. The instantaneous power delivered to the body as a function of time $t$ is:

• A. $\frac{{mv}_1^2}{T_1^2}t$
• B. $\frac{{mv}_1}{T_1^2}t$
• C. ${\left(\frac{{mv}_1}{T_1}\right)}^{2}t$
• D. $\frac{{mv}_1^2}{T_1}{t}^2$

Answer 1

Answer: (A)

$\frac{{mv}_1^2}{T_1^2}t$

Let a be the constant acceleration

Using 1st equation of motion

$v_1=u+a{T}_1$

$v_1=0+a{T}_1$

$a=\frac{v_1}{T_1}..........\left(i\right)$

At any instant t, the velocity v of the body

$v=0+at$

$v=\frac{v_1}{T_1}\cdot t.........\left(ii\right)$

$\because P=Fv$

$P=mav$

$P=m\left(\frac{v_1}{T_1}\right)(\frac{v_1}{T_1}\cdot t)$

$P=\frac{m{v}_1^2}{T_1^2}t$