Question

A car of mass 1200 kg travelling at 72 km/h is brought to rest in 80 meters.
(a) Find the average braking force on the car.
(b) What has happened to the original kinetic energy?

Answer 1

mass = 1200 kg

$speed = 72 \: kmh ^{ - 1} = 20m {s}^{ - 1}$

according to third equ. of motion,

${v}^{2} = {u}^{2} + 2as$

${0}^{2} = {20}^{2} + 2 \times a \times 80$

$a = \frac{ - 400}{2 \times 80}$

$a = \frac{ - 200}{80}$

$a = \frac{ - 5}{2} m {s}^{ - 2}$

$force = mass \times acceleration$

$force = 1200 \times ( \frac{ - 5}{2} )$

$force = - 3000 \: newton$

the original kinetic energy is,

$\frac{1}{2} \times m \times {v}^{2}$

$= 240000 \: joule$

and the energy required to stop the car is

$f \times d$

$= - 3000 \times 80$

$240000 \: joule$

so kinetic energy comes to zero

as same energy applied in other direction

to stop the car