Question

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

• A. $m{v}_1/t_1$
• B. $m{v}_1^2/t_1$
• C. $m{v}_1{t}^2/t_1$
• D. $m{v}_1^{2}t/2t_1^2$

Answer 1

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

Power,

$P=\frac{W}{t}$

$=\frac{Fs}{t}$

$=\frac{\left(ma\right)[ut+\frac{1}{2}a{t}^2]}{t}$

$=\frac{(m\times \frac{v_1}{T_1})[0+\frac{1}{2}\times \frac{v_1}{T_1}\times t^2]}{t}$

$\therefore P=\left(\frac{1}{2}\right)m{\left(\frac{v_1}{T_1}\right)}^{2}t$