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# 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. - CBSE Class 9 - Science

ConceptMathematical Formulation of Second Law of Motion

#### Question

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, = 4 s

According to the first equation of motion:

v = u + at

5 = 25 + a (4)

a = − 5 m/s2
Negative sign indicates that its a retarding motion i.e. velocity is decreasing.

Change in momentum = mv − mu = m (vu)

= 1200 (5 − 25) = − 24000 kg m s−1

Force = Mass × Acceleration

= 1200 × − 5 = − 6000 N

Acceleration of the motor car = − 5 m/s2

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

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