Question

When you try to stop your car in an emergency, there is some time before you can react. Your car is going 25 m/s and your reaction time is 0.20 s, then after you hit your brakes it decelerates at 9.5 m/s2. How far will your car travel before it stops?

Answer 1

During the first 0.2s, before your reacted, the car had passed

$$d_1 = 25m/s\times 0.2s = 5m$$

After you hit the brakes it decelerates in the following time before the full stop:

$$v_0 = at\\ t = \dfrac{v_0}{a}$$

where $v_0 = 25m/s$ and $a = 9.5m/s^2$.

In this time the car passes the following distance:

$$d_2 = v_0t - \dfrac{at^2}{2} = \dfrac{v_0^2}{a} - \dfrac{v_0^2}{2a} = \dfrac{v_0^2}{2a}$$

Obtain:

$$d_2 = \dfrac{v_0^2}{2a} = \dfrac{25^2}{2\cdot 9.5} \approx 32.9m$$

The full distance:

$$d = d_1 + d_2 = 5+32.9 = 37.9m$$

Answer. 37.9 m.