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.
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/s2
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/s2
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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Akhtar, Kiran and Rahul were riding in a motorcar that was moving with a high velocity on an expressway when an insect hit the windshield and got stuck on the windscreen. Akhtar and Kiran started pondering over the situation. Kiran suggested that the insect suffered a greater change in momentum as compared to the change in momentum of the motorcar (because the change in the velocity of the insect was much more than that of the motorcar). Akhtar said that since the motorcar was moving with a larger velocity, it exerted a larger force on the insect. And as a result the insect died. Rahul while putting an entirely new explanation said that both the motorcar and the insect experienced the same force and a change in their momentum. Comment on these suggestions
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