Question

The graph below shows power $\left(P\right)$ delivered by the engine of a car as a function of time.


Find out the final velocity of car, if initial velocity of the car is $10\text{m/s}$ and mass is $200\text{kg}$.

• A. $5\sqrt{10}\text{m/s}$
• B. $5\sqrt{5}\text{m/s}$
• C. $20\text{m/s}$
• D. $15\text{m/s}$

Answer 1

The correct option is A $5\sqrt{10}\text{m/s}$

Work done by engine of car $=\int P.dt$
i.e Work done = Area under the $P-t$ curve
$=\frac{1}{2}[20+10]\times 1000=15000\text{J}$

From work energy theorem,
$\Delta$K.E $=$ Work done
$\frac{1}{2}m{v}_f^2-\frac{1}{2}m{v}_i^2=15000$
$⟹\frac{1}{2}\times 200\times (v_f^2-{10}^2)=15000$
$⟹100v_f^2=15000+10000=25000$
$⟹v_f^2=250$
$⟹v_f=5\sqrt{10}\text{m/s}$