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

Answer

`5 m s ^(-2); 2400 kg ms ^(-1)`;6000 N

Explanation

Mass of the motor car, m = 1200 kg
Initial velocity of the motor car, u = 90 km/h = 25 m/s
Final velocity of the motor car, v = 18 km/h = 5 m/s
Time taken, t = 4 s
According to the first equation of motion:
v = u + at
`implies5 = 25 + a (4)`
` impliesa = - 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 ms^(-1) `
`:.` Force = Mass `xx` Acceleration
`= 1200 xx - 5 = - 6000 N `
Acceleration of the motor car `= - 5 m//s^(2)`
Change in momentum of the motor car `= - 24000 kg ms^(-1)` Hence, the force required to decrease the velocity is 6000 N. (Negative sign indicates retardation, decrease in momentum and retarding force)