# A motorcar of mass 1200kg is moving along a straight line with a uniform velocity of 90 km//h. Its velocity is slowed down to 18 km//h in 4s b

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

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Correct Answer - 5 m s ^(-2); 2400 kg ms ^(-1);6000 N
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
implies5 = 25 + a (4)
 impliesa = - 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 ms^(-1)
:. Force = Mass xx Acceleration
= 1200 xx - 5 = - 6000 N
Acceleration of the motor car = - 5 m//s^(2)
Change in momentum of the motor car = - 24000 kg ms^(-1) Hence, the force required to decrease the velocity is 6000 N. (Negative sign indicates retardation, decrease in momentum and retarding force)