# Deceleration, velocity, acceleration, distance

1.

You are driving toward a traffic signal when it turns yellow. Your speed is the legal speed limit of v0=55 km/h.: your best deceleration rate has the magnitude a = 5.18 m/s^2. Your best reaction time to begin braking is T = .75S. To avoid having the front of your car enter the intersection after the light turns red, should you brake to a stop or continue to move at 55 km/h if the distance to the intersection and the duration of the yellow light are a) 40 m and 2.8 s, and b) 32 m and 1.8s? Give an answer of brake, continue, either (if either strategy works) or neither (if neither strategy works and the yellow duration is inappropriate).

2.
x = x0 + v0 t + .5at^2

any derivatives needed...dx/dt? dv/dt?

3.

well the first thing i tried was converting the 55 km/h to the correct units of m/s. so 55 km/h = roughly about 15.277778 m/s.

then i drew some pictures and realized i need to use a formula involving v0, time, distance, and acceleration. i'm just confused on how to use T=.75 s. i'm getting a physics tutor soon, but since i don't have one yet...i need a lot of help. i just don't even know where to begin.

## Answers and Replies

I believe you can use the reaction time to calculate the distance you travel before applying the brake. You should be able to find the answer if you just use the equation you have quoted I don't think derivatives are required. 