The question
Name: ______________________ Date: ____________ How far does a car need to stop? (10 points)
Experimental setup
A driver brakes for a hazard
A car moves along a straight, level road at a constant speed v₀. At time t = 0 the driver sees a hazard ahead. For a reaction time tr the car keeps moving at v₀; then the driver brakes, and the car slows with a constant acceleration of magnitude a until it stops. The total stopping distance D is measured from where the car is at t = 0 to where it stops. Take the direction of motion as positive.
(a) Sketch a graph of the car's velocity as a function of time from t = 0 until it stops. Label the times tr and the time ts when the car stops, and the velocity v₀. [3 points]
(b) Derive an expression for the total stopping distance D in terms of v₀, tr, a and physical constants, as appropriate. Begin your derivation by writing a fundamental equation or by naming what a feature of your graph represents. [3 points]
(c) Calculate the stopping distance for v₀ = 24 m/s, tr = 0.75 s and a = 6.0 m/s². [2 points]
(d) A student claims: "If the car were going twice as fast, it would need twice the stopping distance." Do you agree or disagree? Justify your answer using your expression from part (b). [2 points]