Suppose you are driving at speed V0 when a sudden obstacle in the road forces yo

Question

Suppose you are driving at speed V0 when a sudden obstacle in the road forces you to make a quick stop. If your reaction time before applying the brakes is tR, what constant deceleration (absolute value of ax), do you need to stop in distance d? Assume that d is larger than the car travels during your reactiont time.

Suppose you are driving 23 m/s when you suddenly see an obstacle 54 m ahead. If your reaction time is .5 seconds and if your car's maximum deceleration is 6.59 m/s^2 can you stop to aviod the collision?

Explanation / Answer

(a)
d=v0tR+v0t+1/2at^2
d=v0(t+tR)+1/2at^2
(b)

you take 0.5 seconds to react, meaning we need to find out how far away you are when you start hitting the breaks.
Distance = Speed*Time
x = (23 m/s)*(0.5 s) = 11.5 m

Now we solve using the new distance you have before the obstacle (54 meters) to find the acceleration necessary. If this is less than or equal to -6.59 m/s^2, then you'll make it.
(v-final)^2 = (v-initial)^2 + (2)*(acceleration)(change in distance)
0 = (23 m/s)^2 + 2*a*(54 m)
-529 m^2/s^2 = 2*a*54
-4.9 m/s^2 = a

This is less than she needs, ergo, you'll avoid the collision.

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