Question

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

• A. $\text{12596 J}$
• B. $\text{10590 J}$
• C. $\text{11592 J}$
• D. $\text{13542 J}$

Answer 1

The correct option is C

$\text{11592 J}$

Mass of the car, $m=\text{1000 kg}$.
The initial velocity of the car, $u=10kmh{r}^{-1}=10\times \frac{5}{18}=2.78m{s}^{-1}$.
Final velocity $v=20kmh{r}^{-1}=20\times \frac{5}{18}=5.56m{s}^{-1}$.
With the mass and velocities,
we can find the initial and final kinetic energies.
$\text{Initial Kinetic Energy}=\frac{1}{2}m{u}^2=\frac{1}{2}\times 1000\times {\left(2.78\right)}^2$
$\text{= 3864.2 J}$
$\text{Final Kinetic Energy}=\frac{1}{2}m{v}^2=\frac{1}{2}\times 1000\times {\left(5.56\right)}^2$
$\text{= 15456.8 J}$
The difference in these values would give us the amount of work done.
$\therefore$Work done = Change in kinetic energy
$\text{= 15456.8 J - 3864.2 J}$
$\text{= 11592.6 J}$