Question

How large an average force is required to stop a 1400-kg car in 5.0 s if the car’s initial speed is 25 m/s?

Answer 1

Answer on Question #40354, Physics, Mechanics | Kinematics | Dynamics

How large an average force is required to stop a 1400-kg car in 5.0 s if the car's initial speed is 25 m/s?

Solution:

The force is defined as the rate of change of momentum for a particular interval of time $t$. It is difficult to find the rate of change if time interval is small. So there comes the term average force.

An average force is the rate of change of momentum over a period of intervals $(\Delta t)$. It is given by

$$F = \frac{m(v_f - v_i)}{\Delta t}$$

Where $m$ is the mass of the body,

$v_f$ is the final speed,

$v_i$ is the initial speed,

$\Delta t$ is the change in time.

Given: Mass of car $m = 1400 \, \text{kg}$

Initial velocity $v_i = 25 \, \text{m/s}$

Final velocity $v_f = 0$

Change in time $\Delta t = 5.0 \, \text{s}$

The average force is given by

$$F = \frac{m(v_f - v_i)}{\Delta t} = \frac{1400 \cdot (0 - 25)}{5} = -7000 \, \text{N}$$

" - "sign indicates that force acts opposite to the direction of motion of a car.

Answer. -7000 N.