Maximize Reaction Time to Avoid Deer: Motorist's Dilemma Explained

[malta]

Homework Statement

A motorist is traveling at l4m/s when he sees a deer in the road 48 m ahead.
If the maximum negative acceleration of the vehicle is -7 m/s^2, what is the maximum reaction time At of the motorist that will allow him to avoid hitting the deer? Answer in units of s.

What i did was divide 48/14 to get the time it would take to get there then using the Vf=Vo+at equation i got a time of 2 and subtracted it from the first time, is that correct??

 

[Delphi51]

No, I don't think so.
I see you realize that there are two different motions to work with.
During the reaction time, before the guy gets his foot on the brake, you have motion at constant speed (zero acceleration). While braking, you have accelerated motion.
You cannot use 48/14 for the first part because the car is not moving at a constant speed of 14 for that distance of 48. If it did, it would hit the deer!

Your work on the accelerated part is correct - it takes 2 seconds to stop. This is a very good start. You must now figure out how far the car goes in these 2 seconds, then use that to find how far the car goes before the braking begins. That will give you the info you need to work out the constant speed part of the motion and find your answer.