Physics

Problem

A car of mass

1000\,\text{kg}

travelling at

30\,\text{m\,s}^{-1}

is brought to rest by a uniform braking force in

5.0\,\text{s}

. A truck of mass

5000\,\text{kg}

undergoes the same change in momentum but is brought to rest uniformly in

20\,\text{s}

. a. (i) Calculate the magnitude of the average braking force acting on the car. b. (ii) Calculate the magnitude of the average braking force acting on the truck. c. (iii) Comment on the numerical difference between the two forces in the light of the time taken to stop each vehicle.

Intuitive explanation

The key insight is that "same change in momentum" means both vehicles experience identical $\Delta p$ , but over different time intervals—so the braking forces are actually different. Use the impulse-momentum theorem ( $F\Delta t = \Delta p$ ) to find each force: since the truck's deceleration is spread over four times longer, its braking force must be one-quarter that of the car. This shows how force and time trade off to produce the same momentum change.

Intuitive explanation

Browse the problem library