You are driving down a straight highway at 20 m/s (72 km/h) on a foggy night. Suddenly you see a truck stopped directly in front of you a distance d down the roadway.
(a) What distance will you have travelled after 1 s? ... After 2 s?

  • Area of the rectangle between 0 s and 1 s is (20 m/s)×1 s = 20 m.
  • Area under the curve between 1 s and 2 s is the area of the rectangle added to the area of the small triangle:
    • Area of rectange: (16 m/s)×1 s = 16 m
    • Area of triangle: (1/2)× (4 m/s)×1 s = 2 m
    Total = 18 m
  • Total displacement between 0 s and 2 s is 20 m + 18 m = 38 m.

Now go on to part (b)

Part (b)

(b) What is the shortest distance d that will allow you to stop before hitting the truck?

What to do

Shade the area representing your total displacement until completely stopped. Then compute the area.
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