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Question
Assume you are driving a car at a constant speed of 82.0 km/h. Suddenly you see a deer standing on the highway and you must put on the brakes. Your reaction time (time elapsed between the moment you see the deer and your foot hitting the brakes) is 0.124 sec. The brakes provide an acceleration of -5.7 m/s2. (a) Find the distance (in m) the car travels (at 82.0 km/h) during your reaction time. (b) Calculate the total distance (in m) traveled by the car before stopping.

I already converted the 82.0km/h to 22.8m/s...

(a):

vf = vi + at
  = 22.8m/s + (-5.7m/s^2)(0.124s)
  = 22.0709778m/s
  = 22.1m/s

(vf^2) = (vi^2) + 2aΔx
(22.1m/s)^2 = (22.8m/s)^2 + 2(-5.7m/s^2)(Δx)
Δx = 2.78m

(b):

(vf^2) = (vi^2) + 2aΔx
(0m/s)^2 = (22.1m/s)^2 + 2(-5.7m/s^2)(Δx)
Δx = 42.73053159m
  = 42.7m

So the total distance would be 2.78m + 42.7m = 45.5m which is apparently incorrect. So could you please explain to me where I went wrong?

Answer
Hello J,

a. You used 2 of the 4 (sometimes 5) formulas of motion. This single formula would have worked as well:
Δx = Vi*t + (1/2)*a*t^2
But you used the wrong value for acceleration. During reaction time, the foot would not be on the brakes. So use a=0.

b. You chose the best formula. Because of the error in part a, your value for Vi was wrong.

Those 2 changes should give you the correct answer.

I hope this helps,
Steve

Physics

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Steve Johnson

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I would be delighted to help with questions up through the first year of college Physics. Particularly Electricity, Electronics and Newtonian Mechanics (motion, acceleration etc.). I decline questions on relativity and Atomic Physics. I also could discuss the Space Shuttle and space flight in general.

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I have a BS in Physics and an MS in Electrical Engineering. I am retired now. My professional career was in Electrical Engineering with considerable time spent working with accelerometers, gyroscopes and flight dynamics (Physics related topics) while working on the Space Shuttle. I gave formal classroom lessons to technical co-workers periodically over a several year period.

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BS Physics, North Dakota State University
MS Electrical Engineering, North Dakota State University

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