A car moving with velocity v has a stopping distance proportional to v².
(a) If a car going 20mi/hr has a stopping distance of 50 feet, what is its stopping distance going 40 mi/hr? What about 60 mi/hr?
(b) After applying the brakes, a car going 30 ft/sec stops in 5 seconds and has v = 30 − 6t. Explain why the stopping distance is given by the area under the graph of v against t.
(c) By looking at areas under graphs of v, explain why a car with the same deceleration as the car in part (b) but an initial speed of 60 ft/sec has a stopping distance 4 times as far.