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

Question

You're driving down the highway late one night at 20 m/s when a deer steps onto the road 47 m in front of you. Your reaction time before stepping on the brakes is 0.50 s, and the maximum deceleration of your car is 10 m/s^2. 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. a = m 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. v =

Explanation / Answer

for car

vox = 20 m/s

D = 47 m

reaction time t = 0.5s

distance travelled in reaction time x1 = vo*t = 20*0.5 = 10 m

distance travelled with deceleration

from vfx^2 - vox^2 = 2*a*x2

0 - 20^2 = -2*10*x2

x2 = 20 m

total distance travelled before stopping = 10 + 20 = 30 m

distance beatween the deer and car after stopping = 47-30 = 17 m

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part (b)

let v be the maximum speed

distance travelled in reaction time x1 = v*t = v*0.5 = v/2 m

distance travelled with deceleration

from vfx^2 - vox^2 = 2*a*x2

0 - v^2 = -2*10*x2

v^2 = 20*x2

x2 = v^2/20

total distance travelled before stopping = x1 + x2 = 40

v/2 + v^2/20 = 40

v = 23.7 m/s <<<<<------answer

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