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.

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Method 1:

Use the formula: Vf^2 - Vo^2 = 2aD

where Vf=0; Vo=11.2 m/s; D=34.7m, then solve for "a"

Once you know "a", use the formula D=Vot + 1/2at^2 to solve for t.

It's a quadratic equation which can be a little hard to solve.

Method 2:

Since this a constant deceleration, you can find out the average speed during the deleration by using Vavg = (Vo + Vf) / 2 where Vo=11.2m/s and Vf=0 to solve for Vavg.

Once you have Vavg and D=34.7m, you can solve for time, t=D/Vavg.