Question

A bob of mass m accelerates uniformly from rest to $v_1$ in time $t_1$. As a function of $t$, the instantaneous, power delivered to the body is :

• A. $\frac{mvit}{t_1}$
• B. $\frac{m{v}_{1}t}{t_1}$
• C. $\frac{m{v}_1{t}^2}{t_1}$
• D. $\frac{m{v}_1^{2}t}{t_1^2}$

Answer 1

The correct option is D $\frac{m{v}_1^{2}t}{t_1^2}$

From $v=u+at$

$v=0+a{t}_i$

$F=ma=\frac{m{v}_1}{t_1}(\because a=\frac{v_1}{t_1})$

Velocity acquired in $tsec=at$

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

Power $=Fv=\left(\frac{m{v}_1}{t_1}\right)\left(\frac{v_1}{t_1}t\right)=\left(\frac{m{v}_1^2}{t_1^2}\right)t$