Problem Youre driving down the highway late one night at 20m

Problem: You\'re driving down the highway late one night at 20m/s when a deer steps onto the road 35m 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.

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

Express your answer using one significant figure.

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

Express your answer using two significant figures.

Please write out each step with explanation. Thank you so much

Solution

1) distance traveled in reaction time,

d1 = u t_reaction = 20 x 0.50 = 10 m

after that Car will travel until it stops (final velocity, v = 0 )

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

0^2 - 20^2 = 2(-10)d2

d2 = 20m

total distance traveled , d = d1 + d2 = 30 m

distance from deer = 35 - 30 = 5 m

(2)Suppose initial speed is u then

d1 =u (0.50) = 0.50 u

after that ,

0^2 - u^2 = 2(-10) (d2)

d2 = u^2 / 20

d1 + d2 = 35

u^2/20 + 0.50u = 35

u^2 + 10u - 700 = 0

u = 21.93 m/s .......Ans