Chapter 8.5, Problem 93E

Three start-ups Three cars. A, B, and C, start from rest and accelerate along a line according to the following velocity functions:

$v_A(t)=\frac{88t}{t+1},v_B(t)=\frac{88t^2}{{(t+1)}^2},\text{and}{v}_C(t)=\frac{88t^2}{t^2+1}.$

1. a. Which car travels farthest on the interval 0 ≤ t ≤ 1?
2. b. Which car travels farthest on the interval 0 ≤ t ≤ 5?
3. c. Find the position functions for each car assuming that each car starts at the origin.
4. d. Which car ultimately gains the lead and remains in front?