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.

(c) Suppose the truck is only 52 m away when you first see it. What will your speed be when you collide?


Try t = 3 s. Then the second shaded area can be divided into two parts:
  1. The top triangle has an area of (1/2)( 8 m/s )( 2 s) = 8 m.
  2. The bottom rectangle has an area of (12 m/s)(2 s) = 24 m
The total is 32 m. The distance travelled from the beginning is 20+32 = 52 m.
The speed at that time is 12 m/s.

Challenge

By asking for the velocity at 52 m we made the math for this problem easy. To find the velocity at any other distance you would use the same ideas. For example:
What is the velocity at 40 m?
Here you can find an approximate answer by using the graph. Try to find the time where the second shaded area is 20 m and read the velocity at that time from the graph. An exact answer can be got by using algebra. As a challenge you can
  • Estimate the time and velocity for a 40 m displacement.
  • Find an exact solution algebraicly. Hint: You have to solve a quadratic equation.

Now what?

There's one more question. Can you stop within 15 m? You can surely answer that one.

That's all!

Go back
Go back go main page