How do I solve this challenging AP Physics mechanics problem?

[beeftrax]

I'm doing an independent study in AP Physics, and am having a lot of trouble with the following problem:

"To stop a car, first you require a certain reaction time to begin braking; then the car slows under the constant braking deceleration. Suppose that the total distance moved by your car during these two phases is 56.7 m when its initial speed is 80.5 km/h, and 24.4 m when its initial speed is 48.3 km/h. What are (a) your reaction time and (b) the magnitude of the deceleration" (Fundamentals of Physics 6th ed; Halliday, Resnick, and Walker; pg 29, #37)

I've set the problem up, graphed the data, manipulated a lot of equations, and tried to solve it geometrically. I suspect that I need to use ratios to relate the two different situations, solve for reaction time, and use that to find acceleration, but I can't see how to do it.

Please Help!

 

[drag]

Greetings !

Use the formula: V^2 = V0^2 +/- 2 * a * x
V - final velocity
V0 - enitial velocity
-a/+a - de/acceleration
x - distance



How to solve : STOP ! DO NOT READ THIS UNLESS YOU TRIED
TO USE THE ABOVE FORMULA (with some small changes) AND
FAILED !





Write the formula for each case. This is how it'll look :

1: V1^2 = V01^2 - 2 * a * (X1 - t * V01)
2: V2^2 = V02^2 - 2 * a * (X2 - t * V02)

X1/X2 - given distances
V01/V02 - given enitial velocities
t - reaction time (unknown)
a - acceleration (unknown)
V1/V2 - final velocities per case => V1 = V2 = 0

Live long and prosper.

 

[beeftrax]

Thanks! You've put my troubled mind at ease.