Question

You're driving down the highway late one night at 20m/s when a deer steps onto the road 60 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. How much distance is between you and the deer when you come to a stop? What is the maximum speed you could have and still not hit the deer?

Answer 1

Initial speed=20m/s

Initial distance b/w driver & the deer is 60m.
Rxn time =0.50 sec

Deceleration =10m/s^2

distance traveled before brakes are applied=20*0.50

distance traveled after brakes are applied=>
using equation v^2=u^2+2as
v=0,u=20 m/s, a=-10 m/s^2

0=400-20s
s=20m

so distance traveled after brakes are applied=20m

Answer 2

net distance traveled before car stops=distance traveled before brakes are applied + distance traveled after brakes are applied

Answer 3

distance b/w car & deer after car stops=60-distance traveled by car before it stops completely.

Answer 4

when the driver will have maximum speed so that the car doesn't hit the deer the distance traveled by it before stopping must be equal to 60m.

Let this maximum speed be 'u'.

Net distance traveled=(u*0.50)+(u^2/2a)=60

a=-10m/s^2

so above eqn becomes

(u*0.50)+(u^2/20)=60
solve for u.This will be the cars maximum speed so that it doesn't hit the deer.