Question

What is the amount of work to be done on a car of mass $1000kg$ to increase its velocity from $10kmh{r}^{-1}$ to $20kmh{r}^{-1}$?

• A. 12596 J
• B. 10590 J
• C. 11592 J
• D. 13542 J

Answer 1

The correct option is C

11592 J

Mass of the car is $\text{1000 kg}$
The initial velocity of the car, $u=10kmh{r}^{-1}=\frac{10\times 1000}{3600}=2.78m{s}^{-1}$
Similarly, the final velocity, $v=20km{hr}^{-1}=\frac{20\times 1000}{3600}=5.56m{s}^{-1}$
With the mass and velocities, we can find the initial and final kinetic energies.
Initial Kinetic Energy $=\frac{1}{2}\times 1000\times {\left(2.78\right)}^2=3864.2J$
Final Kinetic Energy $=\frac{1}{2}\times 1000\times {\left(5.56\right)}^2=15456.8J$
According to work energy theorem, the difference in kinetic energies would give us the amount of work done.
$\Rightarrow$ Work done = Change in kinetic energy = $15456.8-3864.2=11592.6J$