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Question

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

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Solution

Mass of the motor car, m = 1200 kg
Initial velocity of the motor car, u = 90 kmph = 25 ms1
Final velocity of the motor car, v = 18 kmph = 5 ms1
Time taken, t = 4 s
According to the first equation of motion:
v = u + at
5 = 25 + a (4)
a = - 5 ms2
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 kgms1
Force = Mass × Acceleration = 1200 × - 5 = - 6000 N
Acceleration of the motor car = - 5 ms2
Change in momentum of the motor car = - 24000 kg ms1
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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