Question

Calculate the work required to be done to stop a car of $1500\mathrm{kg}$ moving at a velocity of $60\mathrm{km}/\mathrm{h}$?

Answer 1

Step 1: Given data

Mass $\left(\mathrm{m}\right)=1500\mathrm{kg}$

Velocity $\left(\mathrm{v}\right)=60\mathrm{km}/\mathrm{hr}$

Step 2: Formula used

Kinetic energy $(\mathrm{K}.\mathrm{E})$$=\frac{1}{2}m{v}^2$

$\mathrm{m}=$Mass

$\mathrm{v}=$velocity

Step 3: Determine the initial kinetic energy
The velocity of the car
$=60\times \frac{5}{18}\mathrm{m}/\mathrm{s}$

$=10\times \frac{5}{3}\mathrm{m}/\mathrm{s}$

$=\frac{50}{3}\mathrm{m}/\mathrm{s}$

Work done = Kinetic energy of the car
Initial Kinetic energy $=\frac{1}{2}{\mathrm{mv}}^2$
$=\frac{1}{2}\times \left(1500\right)\times {\left(\frac{50}{3}\right)}^2$

$=\frac{1}{2}\times 1500\times \left(\frac{50}{3}\times \frac{50}{3}\right)$

$=\frac{1}{2}\times 1500\times \frac{2500}{9}$

$=\frac{500\times 2500}{3\times 2}$

$=\frac{250\times 2500}{3}$

$=208333.3\mathrm{J}$

Step 4: Determine the work done

Since the car eventually stops

Final kinetic energy $=0$

Now,

Work done $=$Change in Kinetic energy
$=208333.3-0$

$=208333.3\mathrm{J}$
Therefore, the work done is $208333.3\mathrm{J}$.