Bob is driving the getaway car after the big bank robbery. He’s going 50 m/s when his headlights suddenly reveal a nail strip that the cops have placed across the road 150 m in front of him. If Bob can stop in time, he can throw the car into reverse and escape. But if he crosses the nail strip, all his tires will go flat and he will be caught. Bob’s reaction time before he can hit the brakes is 0.60 s, and his car’s maximum deceleration is 10 m/s². Does Bob stop before or after the nail strip? By what distance?

The speed of the bike is $v_i=50m/s$

The reaction time is $t=0.6sec$

The distance of the nail strip from the bike islocalid="1648454455073" $S=150m$

The acceleration of the bike is $a=-10m/s^2$

Since the reaction time is 0.6 sec. The distance covered by the bike in this reaction time is given by

$$\begin{gathered} D=v_{i}t \\ D=50(0.6) \\ D=30m \end{gathered}$$
Therefore, this is the distance Bob covers before he applies break.
This implies that the rest of the road is covered by a nail strip. The width of nail strip is $S-D=150-30=120m$

Now, the final velocity of the bike is $v_f=0m/s$

Using the equation of motion,

localid="1648454482302" $$\begin{gathered} {\left(v_f\right)}^2-{\left(v_i\right)}^2=2aS\text{'} \\ 0-{\left(50\right)}^2=2(-10)S\text{'} \\ S\text{'}=\frac{2500}{20}=125 \\ S\text{'}=125m \end{gathered}$$
Therefore, the distance covered by the bike after applying breaks is 125 m.

This distance is more than the total width of the nail strip i.e. 120m . Therefore, Bob would get caught by the police as he crosses the nail strip.
The distance Bob stops after the nail strip is $125-120=5m$