The position of a car traveling along a straight road is modeled (for seconds) by the…

MATHEMATICS · Multi-part · AP · Calculus AB · Contextual Applications of Differentiation · Contextual Applications of Differentiation

Problem

The position of a car traveling along a straight road is modeled (for

0\le t\le 4

seconds) by the polynomial

s(t)=5t^{4}-20t^{3}+15t^{2}+10

, where

s

is measured in meters and

t

in seconds. (a) Determine the velocity function

v(t)

. (b) Compute the acceleration of the car at

t=2

seconds. (c) Find all times in

0\le t\le 4

when the car is at rest. (d) On which subintervals of

[0,4]

is the car moving in the positive direction? Justify your answer. (e) At

t=1

second, is the car’s speed increasing or decreasing? Explain by comparing the signs of velocity and acceleration.