### Quadratic Equations and Driving

Many drivers make the assumption that braking distance would be directly proportional to their speed. We shall investigate this by using some simple quadratic equations.

From our kinematic equation

v^2=u^2+2as,

we want to estimate our braking distance d, hence v=0. If we include reaction time t, we get

d=u^2/2a+ut

Assume a= 10m/s/s and t = 0.75s for an average driver. Then we have

d=u^2/20+(0.75)u

If a vehicle speeds at 100km/h (27.8m/s), d=59.5m

If a vehicle slows down to half that speed, ie 50 km/h (13.9m/s), d=20.1 m, which is roughly one third of the original distance, and not half of the latter!

Quadratic equations apply to our everyday lives, and this being one example. Students can be given tasks such as investigating how reaction time affects the braking distance, and why it is important for drivers to slow down in congested areas, and why drivers should never tail gate or use their handphones while driving (distractions can increase their reaction times to 3s or more.)

More can be found in this link:

http://www.science.org.au/nova/058/058key.htm

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