Question

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

Answer 1

Mass of the motor car, m = 1200 kg
Initial velocity of the motor car, u = 90 $kmph$ = 25 $m{s}^{-1}$
Final velocity of the motor car, v = 18 $kmph$ = 5 $m{s}^{-1}$
Time taken, t = 4 s
According to the first equation of motion:
v = u + at
5 = 25 + a (4)
a = - 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$m{s}^{-1}$
Force = Mass $\times$ Acceleration = 1200 $\times$ - 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 retardation, decrease in momentum and retarding force.)