Question 4

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.

Answer

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

Initial velocity of the motor car, *u* = 90 km/h = 90 x 5/18 = 25 m/s

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

Time taken, *t* = 4 s

Using the first equation of motion:

*v = u + at*

5 = 25 + a (4)

a = -5 m/s^{2}

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 the retardation, decrease in momentum and retarding force respectively)

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