You\'re driving down the highway late one night at 20m/s when a deer steps onto

Question

You're driving down the highway late one night at 20m/s when a deer steps onto the road 43 m in front of you. Your reaction time before stepping on the brakes is 0.50s, and the maximum deceleration of your car is 10m/s2.

a) How much distance is between you and the deer when you come to a stop?

Express your answer to two significant figures and include the appropriate units.

b) What is the maximum speed you could have and still not hit the deer?

Express your answer to two significant figures and include the appropriate units.

Explanation / Answer

a] distance covered in time t = 0.5s,

d = vt = 20(0.5) = 10 m

then, a = - 10 m/s2 and final velocity v = 0 m/s

now use, S = (v2 - u2)/2a

=> S = 20 m

so, total distance covered until stopping of the car is: D = d + S = 30 m

therefore, distance between the deer and the car is: 43 - 30 = 13 m.

b] minimum distance between the deer and the car should be 0 m.

so, D = 43 m

therefore, S = 33 m

using a = - 10 m/s2 and v = 0 m/s, this gives:

u = 25.690 m/s.

this is the maximum speed you can have and not hit the deer.

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