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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.

Given, mass of the car (m) = 1200 kg

Initial velocity (u) = 90 km/hour = 25 meters/sec

Terminal velocity (v) = 18 km/hour = 5 meters/sec

Time period (t) = 4 seconds

So, the acceleration of the car,
$$\therefore a = \frac{v-u}{t} \$$
$$\Rightarrow \ a = \frac{5-25}{4} \$$
$$\Rightarrow \ a = -5 \ m/s^2$$

Therefore, the acceleration of the car is $$-5 m/s^2$$ .

Initial momentum of the car
= m × u
= (1200kg) × (25m/s)
= 30,000 kg m/s

Final momentum of the car
= m × v
= (1200) × (5)
= 6,000 kg m/s

$$\therefore$$ change in momentum (final momentum – initial momentum)
= (6,000 – 30,000)
= -24,000 kg m/s

External force applied
= mass of car × acceleration
= (1200) × (-5) = -6000 N