The position of a car

MATHEMATICS · Single correct · CBSE · Mathematics · Applications of Derivatives · Applications of Derivatives

Problem

The position

s(t)

of a car, measured in meters, is differentiable for

t \ge 0

seconds. At

t = 4

, the derivatives satisfy

s'(4) = 20

and

s''(4) = -3

. Which statement is most consistent with this information about the car’s motion at

t = 4

seconds? (a) The car is moving backward at

20\,\text{m/s}

and its speed is decreasing at

3\,\text{m/s}^2

. (b) The car is moving forward at

20\,\text{m/s}

and its speed is decreasing at

3\,\text{m/s}^2

. (c) The car has traveled

20\,\text{m}

and its acceleration is

-3\,\text{m/s}^2

. (d) The car is moving forward at

20\,\text{m/s}

and its speed is increasing at

3\,\text{m/s}^2