Kinematics - Constant Deceleration

[rtsphysics]

Homework Statement

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

Homework Equations

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 don't 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 don't know a or t...

Any help would be appreciated!

 

[madah12]

you don't need an equation for the final velocity ,for it is given by statement of "to stop a car".

 

[thepatient]

Try setting all your units equal to each other. Make sure you are not setting feet equal with miles and hours with seconds. Convert feet to miles or miles/hr to feet/hr. All units of time should be the same unit and all the units of distance should be the same.