Question

I am coasting along a highway at 30.0 m/s when I suddenly see a deer frozen in its tracks in front of me, 200 meters away. At what rate must I slow down to ensure I do not hit the deer. Assume I have a reaction time of 0.30 seconds.

Answer 1

To avoid hitting the deer, you need to slow down at a rate of approximately 4.71 m/s².

Step-by-step explanation:

To calculate the rate at which you must slow down to avoid hitting the deer, you need to consider the distance and time available, as well as your reaction time. Given that you are traveling at 30.0 m/s and the deer is 200 meters away, you have 6.67 seconds to react before reaching the deer. Considering a reaction time of 0.30 seconds, you have 6.37 seconds to slow down.

Using the equation: acceleration = (final velocity - initial velocity) / time, you can calculate the rate at which you need to slow down. Let's assume the final velocity is 0 m/s (since you need to come to a stop).
acceleration = (0 - 30.0) / 6.37 = -4.71 m/s²

Therefore, you need to slow down at a rate of approximately 4.71 m/s² to ensure you do not hit the deer.

Answer 2

Answer:a=-4044.4m/s²

Step-by-step explanation:

S=300m

Vs=300m/s

t=0.3s

Use equation that connects distance and acceleration

S=Vs*t-a*t²/2

200=30*0.3-a*0.09/2

200=9-a*0.045

182=-a*0.045

a=-4044.4m/s²