What is the maximum speed you could have and still avoid hitting the deer?

[xfaceless]

Homework Statement

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?

Homework Equations

vf^2=vi^2+2ad

The Attempt at a Solution

I figured out part a) by calculating the actual distance the deer is infront of your car (by using reaction time given), and then solved for the distance you travel after you hit the brakes using the kinematics equation.
so, the distance between you & the deer when your car comes to a stop is 22.5m.

For part b), .. I don't really understand part b). I tried solving for vi by putting vf at 0, a=-12, and d=36 but that didn't lead to the right answer. I got vi=29.4m/s which is wrong.

Any help please ? ):

 

[CAF123]

Assuming the same reaction time, you can use the same equation you used in part a), but this time making the initial speed of the car an unknown. You will want the total distance traveled to be less than the 45m, so as to not hit the deer.

I think in your attempt, you assumed he was going at 18m/s in the distance covered during reaction time.

 

[xfaceless]

For part b) I did this..
vf^2=vi^2+2ad
0=vi^2+2(-12)(45)
vi=33m/s.
But that's incorrect..
I still dont' get it. :T

 

[Ibix]

Now you're giving the car 45m of braking distance - in other words 0 reaction time. If you've got 45m total, and you travel at v_i for 0.5s before decelerating, how much distance have you got for braking?

A quick sketch of velocity versus time, and distance versus time can really help to visualise this.

 

[xfaceless]

Nevermind. I got it.

 

[xfaceless]

Thanks everyone.