Question

Q3. A bus and car, both moving with kinetic energy 10,000 J are retarded by applying
brakes so that now both are moving with kinetic energy 5,000 J. If the distance travelled by
both the bus and the car is 50 m during this change in kinetic energy, find the ratio of the
retarding forces acting on them.


Only proper steps and calculations​

Answer 1

Given:

A bus and car, both moving with kinetic energy 10,000 J are retarded by applying brakes so that now both are moving with kinetic energy 5,000 J. The distance travelled by both the bus and the car is 50 m.

To find:

Ratio of retarding forces.

Calculation:

In this type of questions , it is best to apply WORK-ENERGY THEOREM :

• This theorem states that the net work done by all the forces will be equal to the change in kinetic energy of the object.

For the bus:

$\therefore \: \Delta KE = work$

$= > \: \Delta KE = F_{(bus)}x$

$= > \: 5000 - 10000 = F_{(bus)}x$

$= > \: - 5000 = F_{(bus)}x$

$= > \: F_{(bus)} = - \dfrac{5000}{x} \: \: \: \: .....(1)$

For Car:

$\therefore \: \Delta KE = work$

$= > \: \Delta KE = F_{(car)}x$

$= > \: 5000 - 10000 = F_{(car)}x$

$= > \: - 5000 = F_{(car)}x$

$= > \: F_{(car)} = - \dfrac{5000}{x} \: \: \: \: .....(2)$

So, the ratio is :

$\boxed{ \bold{ \large{ F_{bus} : F_{car} = 1 : 1}}}$