To stop a car, you require first a certain reaction time to begin braking; then the car slows down under the constant braking deceleration. Suppose that the total distance moved by your car during these two phases is 186 ft when its initial speed is 50 mi/hr, and 80 ft when its initial speed is 30 mi/hr. What are (a) your reaction time and (b) the magnitude of the deceleration?
Problem taken from Fundamentals of Physics 5th ed. Halliday, Resnick, Walker Pg. 32, prob. 51P
x - x0 = 0.5(v0 + v)t
x - x0 = vt - 0.5at2
v2 = v02 + 2a(x - x0)
The Attempt at a Solution
Ok so I tried plugging in the displacements 186 ft and 80 ft into the above equations. The acceleration is constant so I can use the equations above. However, when i plug it in, I always get two or more equations with at least two variables. For example, plugging both numbers in the first equation, we get:
186 ft = 0.5(50mi/hr + v1)t1
80 ft = 0.5(30mi/hr + v2)t2
I dont see how I can get one of the unknown variables such as final velocity using any other equations, such as v = v0 + at, since i dont know a or t....
Any help would be appreciated!