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.

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 = ˆ’ 5 m/s2
Negative sign indicates that its a retarding motion i.e. velocity is decreasing.
Change in momentum = mv ˆ’ mu = m (vˆ’u)
= 1200 (5 ˆ’ 25) = ˆ’ 24000 kg m sˆ’1
Force = Mass — Acceleration
= 1200 — ˆ’ 5 = ˆ’ 6000 N
Acceleration of the motor car = ˆ’ 5 m/s2
Change in momentum of the motor car = ˆ’ 24000 kg m sˆ’1
Hence, the force required to decrease the velocity is 6000 N.
(Negative sign indicates retardation, decrease in momentum and retarding force)

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