You're driving down the highway late one night at 18m/s when a deer steps onto the road 45m in front of you. Your reaction time before stepping on the brakes is 0.50s , and the maximum deceleration of your car is 12m/s^2.

a) How much distance is between you and the deer when you come to a stop?b) What is the maximum speed you could have and still not hit the deer?

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Your reaction time is 0.50 sec, meaning that you have advanced by 0.50*18, i.e. 9 m by the time of your spottting the deer and before you actually press the brakes.

That makes the actual distance between your car and the deer = (45-9)=36 m at the point of your hitting the brakes.

When you come to a stop, v=0. Applying maximum allowable deceleration, from the laws of motion,

`v^2=u^2-2*a*s`

So, `0=18^2-2*12*s`

`rArr s=18^2/(2*12) `

`=13.5 ` m

Your car rolls over this distance before coming to a stop, after you had hit the brakes.

a) The distance between you and the deer when your car comes to a stop is therefore, 36-13.5= **22.5** m.

b) The maximum speed you could have and still not hit the deer can be obtained by taking the roll over distance equal to 36 m, in the same relationship such that

`0=u^2-2*12*36`

`rArr u=sqrt(2*12*36)`

`=29.4 ` m/s.

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