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.

 

[tomcue]

I would like to first clarify that reaction time is the time it takes for a person to respond to a stimulus, in this case, the sighting of the deer. It is not the same as braking time, which is the time it takes for the vehicle to come to a complete stop after the brakes are applied.

To answer the question, we can use the equation d = Vot + 1/2at^2, where d is the distance, Vo is the initial velocity, a is the acceleration, and t is the time. In this scenario, the distance to the deer is 48 m, the initial velocity of the vehicle is 14 m/s, and the acceleration is -7 m/s^2. We can rearrange the equation to solve for time, which gives us t = (Vo ± √(Vo^2 - 2ad))/a. Plugging in the values, we get t = (14 ± √(14^2 - 2(-7)(48)))/(-7) = 2.37 s or -0.37 s. Since we cannot have a negative time, the maximum reaction time for the motorist is 2.37 seconds.

Your approach of dividing the distance by the initial velocity is not entirely correct, as it does not take into account the acceleration of the vehicle. It would give you an approximate estimate, but the more accurate method would be to use the equation mentioned above. Additionally, it is important to note that in real-life situations, reaction time can vary based on individual factors such as alertness, distractions, and fatigue.