Stopping distance and speed

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Question from Joanna, a student:

The algebraic relation d=0.0056^2 + 0.14s models the relation between a vehicle's stopping distance d, in metres, and its speed s, in kilometres per hour.
(a) What is the fastest you could drive and still be able to stop within 80 m?
(b) What is the stopping distance for a car travelling at 120 km/h?
(c) Estimate the length of an average car. How many car lengths does the the stopping distance in (b) correspond to?

Joanne,

For part (a), you can substitute 80 in for d in the equation. So you have 80 = 0.0056 s^2 + 0.14 s and you can solve this
quadratic equation by using the quadratic formula to find the corresponding value of s (the speed).

Part (b) is much easier than (a): you substitute 120 in for s and your equation is d = 0.0056 (120)^2 + 0.14 (120) and you can just calculate d.

Cheers,
Stephen La Rocque.

Math Central is supported by the University of Regina and The Pacific Institute for the Mathematical Sciences.