Question

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.

Answer 1

Mass of the motor car, m = 1200 kg

The initial velocity of the motor car, u = 90 km/h^-1

= `90 xx 5/18`

= 25 ms^-1

The final velocity of the motor car, v = 18 km/h^-1

= `18 xx 5/18`

= 5ms^-1

Time taken, t = 4 s

(i) Acceleration, a = `"Change in velocity"/ "Time"`

= `(v - u)/t`

= `(5 - 25)/4`

= -5 ms^-2

 (ii) Change in momentum

= mv = mu = m (v - u)

= 1200 (5 - 25)

= -24000 kg ms^-1

The magnitude of change in momentum

= 24000 kg ms^-1

(iii) Force, F = ma

= 1200 (-5)

= -6000 N

∴ Magnitude of force = 6000 N