When you see a traffic light turn red, you apply the brakes until you come to a stop. Suppose your initial speed was 11.2 m/s, and you come to rest in 34.7 m. How much time does this take? Assume constant deceleration.

Question

jamesj · Answer

Let v be the velocity and a the constant deceleration.  Then 
$$ v = 11.2 - at $$
This also means that the displacement s is
$$ s = 11.2t - at^2/2 $$

You now have two equations.  You're also given two pieces of information.  Suppose it takes t = T time to stop.  Then you know that v = 0 when t = T,
$$ 0 = v = 11.2 - at $$
You also know that this happens when s = 34.7.

Hence you have two equations, two unknowns.  Solve them for T and you'll find a as well.

jamesj · Answer

you there?  Make sense?

jamesj · Answer

To make it even more explicit, the two equations are
$$ 0      = 11.2 - aT $$ $$
34.7 = 11.2T - aT^2/2 $$