Question

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 120 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 0.7 s,and his car's maximum deceleration is 10 m/s2.Does Bob stop before or after the nail strip and by what distance?Express your answer with the appropriate units. Enter positive value if Bob stops after the nail strip and negative value if he stops before it.

Answer 1

Answer:

-40 m

Explanation:

First, we find the position that Bob reaches before he reacts.

x = x₀ + v₀ t + ½ at²

x = 0 m + (50 m/s) (0.7 s) + ½ (0 m/s²) (0.7 s)²

x = 35 m

Then, we find his position when he stops after deceleration.

v² = v₀² + 2a(x - x₀)

(0 m/s)² = (50 m/s)² + 2(-10 m/s²)(x - 35 m)

x = 160 m

His position relative to the nail strip is:

120 m - 160 m = -40 m

So Bob stops after the nail strip by 40 m.