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.

Solution

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

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

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

Time period (t) = 4 seconds

Therefore, the acceleration of the car is -5 ms^-2.

Initial momentum of the car = m × u = (1200kg) × (25m/s) = 30,000 kg.m.s^-1

Final momentum of the car = m × v = (1200kg) × (5m/s) = 6,000 kg.m.s^-1

Therefore, change in momentum (final momentum – initial momentum) = (6,000 – 30,000) kg.m.s^-1

= -24,000 kg.m.s^-1

External force applied = mass of car × acceleration = (1200kg) × (-5 ms^-2) = -6000N

Therefore, the magnitude of force required to slow down the vehicle to 18 km/hour is 6000 N