Question

A car of mass 1200 kg is moving along a straight line with a uniform velocity of 90 $\frac{km}{h}$. Its velocity is slowed down to 18 ${kmh}^{-1}$​ in 4 s by an unbalanced external force. Calculate the change in momentum and the magnitude of the force required.

Answer 1

Step 1: Calculate the acceleration of the car

Initial velocity of the car (u) = 90 ${kmh}^{-1}$​​ = 25 ${kmh}^{-1}$​​

Final velocity of the car (v) = 18 ${kmh}^{-1}$​​ = 5 ${ms}^{-1}$​​

Time (t) = 4 s

Acceleration (a) =?

We know, v = u + a t

5 = 25 + a $\times$ 4

a $\times$ 4 = - 20

a = -5 ${ms}^{-2}$​​

Step 2: Calculate change in momentum

p = m (v - u) = 1200 (5 - 25) = 1200 $\times$ (-20) = -24000 Ns

Step 3: Calculate the magnitude of force

Magnitude of force F = $\frac{m(v-u)}{t}$ = - 6000 N