Checking Your Answer

This is a very important step in the solution process since it will tell you whether your answer, which is an estimate, is close to the correct answer.

To check your solution, three things should be true about your distance function d(t):

  1. d(0) = 0, since distance started from where the car started it's skid,
  2. d'(0) = 88, since the car started skidding with an initial speed of 88 ft/sec, and
  3. d''(t) = -20, since the car's given acceleration is -20 ft/sec.
Note that your results might differ from the exact results, given in the above list, since you're just making estimates and guessing at functions based on those estimates.

For example, suppose the distance function you found is

d(t) = -15t2 + 30t

Then d(0) = 0, but d'(t) = -30t + 30 so d'(0) = 30 not 88 and d''(t) = -30 not -20, so this distance function d(t) cannot be even close to correct.

Again, since your d(t) is found from estimates of areas and interpolation of points, then your d(t) may not be exact but rather close enough. But what is close enough?

So, if you find that your distance function is not close to correct, then you should go back and try to do it all again.

Next: Follow the "Analytical Solution" link to the left.