Lab Activity: Reaction Time Solution

     In the calculation below I used a reaction time of 0.25 seconds. Your reaction time was most likely less and your answer for the minimum distance would also be less than mine. I made the assumption that the negative acceleration doesn't kick in until your foot hits the brake and once it does, the deceleration is constant.

First find the distance traveled at 20 m/s prior to hitting the brake. Assume no acceleration as your foot moves to the brake pedal. Use the second kinematic equation:
Δx = v_ot + ½at²
Δx = 20(0.25) + ½(0)(0.25)²
Δx = 5.0 m

Now determine the amount of distance for the car to stop once your foot hits the brake. Use the fourth kinematic equation.
v² = v_o²+ 2aΔx
0 = (20)² + 2(-4.6)Δx
Δx = 43.5 m

Total distance = 5.0 + 43.5 = 48.5 m

If the deer was further from you (at t=0) than 48.5 m you would not hit the deer.