Question

A car with mass 1 500 kg moves with costant velocity of 36 ms^-1. The driver sees a group of cows in front and he immediately steps on the brake pedal and manages to stop the car in 6 seconds. The distance of the cows from the car when the driver spotted them was 160 m. How far are the cows from the car when the car stops.

Answer 1

Let $d=160\ m$ is the distance from the car to the cows when the driver was spotted them, $d_1$ is the stopping distance of the car and $d_2$ is the distance from the car to the cows when the car stops. Let's first find the deceleration of the car from the kinematic equation:

$$v=v_0+at,$$ $$a=\dfrac{v-v_0}{t}=\dfrac{0-36\ \dfrac{m}{s}}{6\ s}=-6\ \dfrac{m}{s^2}.$$

Then, we can find the stopping distance of the car from another kinematic equation:

$$v^2=v_0^2+2ad_1,$$ $$d_1=\dfrac{v^2-v_0^2}{2a}=\dfrac{0-(36\ \dfrac{m}{s})^2}{2\cdot(-6\ \dfrac{m}{s^2})}=108\ m.$$

Finally, we can find the distance from the car to the cows when the car stops:

$$d=d_1+d_2,$$ $$d_2=d-d_1=160\ m-108\ m=52\ m.$$