A motorcar of mass 1200 kg is moving along a straight line with a uniform velocity of 90 km/h. Its velocity is slowed down to 18 km/h in 4 s by an unbalanced external force. Calculate the acceleration and change in momentum. Also calculate the magnitude of the force required.

#### Solution

Mass of the motor car, *m* = 1200 kg

Initial velocity of the motor car, u = 90 km/h = 25 m/s

Final velocity of the motor car, *v* = 18 km/h = 5 m/s

Time taken, *t *= 4 s

According to the first equation of motion:

*v* = *u* + *at*

5 = 25 + a (4)

*a* = − 5 m/s^{2}

Negative sign indicates that its a retarding motion i.e. velocity is decreasing.

Change in momentum = *mv* −* mu* = *m* (*v*−*u*)

= 1200 (5 − 25) = − 24000 kg m s^{−1}

Force = Mass × Acceleration

= 1200 × − 5 = − 6000 N

Acceleration of the motor car = − 5 m/s^{2}

Change in momentum of the motor car = − 24000 kg m s^{−1}

Hence, the force required to decrease the velocity is 6000 N.

(Negative sign indicates retardation, decrease in momentum and retarding force)