Question

Calculator question: Suppose a car is moving with increasing speed according to the following table.
time(sec) 0 2 4 6 8 10
speed(ft/sec) 30 36 40 48 54 60
The closest approximation of the distance traveled in the first 10 seconds is
(A) 150 ft (B) 250 ft (C) 350 ft (D) 450 ft (E) 550 ft
Answer is D. Please explain how to get to the answer. Thank you!

Answer 1

What you can do is calculate the underestimate and overestimate to approximate the distance. Since we know the car is travelling at increasing speed but do not know for sure when or which second it accelerates, we can approximate by finding underestimate and overestimate and the average of the two. We know Distance = Speed x Time and the data is in increment of 2 seconds,
Underestimate would be
30(2)+36(2)+40(2)+48(2)+54(2) = 416

Overestimate would then be:
36(2)+40(2)+48(2)+54(2)+60(2) = 476

The average of the two would be 446 so D = 450 is the closest.

Answer 2

Refer to the attached solution. Mathematica 9 was used for the plots and calculations.