You are cruising on a freeway at 30 m/s, when you suddenly notice traffic stoppe

Question

You are cruising on a freeway at 30 m/s, when you suddenly notice traffic stopped in front of you and need to come to a complete stop. (a) If the friction between your car's tires and the road can provide enough decelerating force for acceleration of a = -9 m/s^2, how much stopping distance do you need, ignoring reaction time for applying the brakes? (b) Under wet conditions (for example, on a rainy day), the friction between the tires and the road is reduced. If the maximum magnitude of acceleration you can apply is now 6 m/s^2, how much stopping distance do you now need? (c) Under normal conditions (maximum magnitude of acceleration is back at 9 m/s^2), suppose you have been speeding at 40 m/s (about 90 mph). How much stopping distance do you now need?

Explanation / Answer

Here ,

initial velocity of car , u = 30 m/s

a)

acceleration, a = -9 m/s^2

Now , let the stopping distance is d

Using third equation of motion

v^2 - u^2 = 2 * a *d

0 - 30^2 = -2 * 9 * d

d = 50 m

the stopping distance is 50 m

b)

for accleration , a = -6 m/s^2

Now , let the stopping distance is d

Using third equation of motion

v^2 - u^2 = 2 * a *d

0 - 30^2 = -2 * 6 * d

d = 75 m

the stopping distance is 75 m

c)

initial speed , u = 40 m/s

acceleration, a = -9 m/s^2

Now , let the stopping distance is d

Using third equation of motion

v^2 - u^2 = 2 * a *d

0 - 40^2 = -2 * 9 * d

d = 88.9 m

the stopping distance is 88.9 m

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