The distance traveled by the car when the brakes are applied.
Answer to Problem 15E
The distance traveled by the car is 155 ft.
Explanation of Solution
Given information:
The velocity with respect to time is a decreasing curve.
The curve lies in the interval between
Use right endpoints as a lower estimate, left end points as an upper estimate, and mid endpoints as mid estimate due to a decreasing velocity curve with respect to time.
The expression to find the distance using mid estimate
Here, the mid height of the first rectangle is
Take interval
Draw six rectangles using mid endpoints for
Refer Figure (1).
Take the mid height of the first rectangle’s
Substitute 6 for n, 55ft/sec for
Therefore, the mid estimate using mid endpoints for
Check whether the estimated value is reasonable or not:
Find the area of triangle (A) as shown below:
Here, the width of triangle is b and the height of the triangle is h.
Refer to Figure (1).
Assume the curve as a triangle by drawing a line from
Take the width of triangle b value as 6 sec and the height of the triangle h value as 70 ft/sec.
Substitute 6 sec for b and 70 ft/sec for h in Equation (2).
The assumed triangle value is an overestimate compared to the calculated mid estimate value as 155 ft.
So the calculated mid estimate is a reasonable value.
Hence, the distance travelled by the car is 155 ft when the brakes are applied.
Chapter 5 Solutions
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