Question

A car of mass 480 kg moving at a speed of 15 m/s is stopped in 10 seconds. Calculate the force applied by the brakes.

Answer 1

Question 30462

The car is moving with negative acceleration. Hence, the law for speed as a function of time is $v(t) = v_0 - at$ , where $v_0$ is initial velocity, and $a$ is acceleration.

According to $2^{\mathrm{nd}}$ Newton's law, acceleration is connected with force exerted on body by $a = \frac{F}{m}$ . Hence, law of motion in terms of force is $v(t) = v_0 - \frac{F}{m} t$ . At the moment of stop $v = 0\frac{m}{s}$ and time is $t = 10s$ . Plugging these values into latter formula, obtain force applied by the brakes:

$$0 = 15 - \frac {F}{m} \cdot t \Rightarrow F = v _ {0} \frac {m}{t} = \frac {15 \frac {m}{s}}{10 \frac {m}{s}} \cdot 480 \, \text{kg} = 720 \, \text{N}.$$