Question

The velocity vs time graph of a body of mass $15\text{kg}$ is shown in the figure. What is the power delivered by net external force acting on body? Consider work done by internal forces to be zero.

• A. $3000\text{W}$
• B. $1000\text{W}$
• C. $375\text{W}$
• D. $500\text{W}$

Answer 1

The correct option is C $375\text{W}$

From the work energy theorem, we have
$\Delta KE=\sum W_{\text{ext}}+\sum W_{\text{int}}$

Considering $\sum W_{\text{int}}=0$
$\Rightarrow \Delta KE=W$
where $W=$ work done by net external force
$\therefore W=K{E}_f-K{E}_i$

$v_f=20\text{m/s},v_i=0\text{m/s}$ from the graph
$\Rightarrow W=\frac{1}{2}m{v_f}^2-0$
$\therefore W=\frac{1}{2}\times 15\times {20}^2=3000\text{J}$

Hence, power delivered ($P$) to body is:
$P=\frac{W}{\Delta t}$
$\Delta t=8\text{s}$; time interval for action of force
$\therefore P=\frac{3000}{8}=375\text{J/s}=375\text{W}$