Chapter 6, Problem 3RE

Displacement, distance, and position Consider an object moving along a line with the following velocities and initial positions. Assume time t is measured in seconds and velocities have units of m/s.

  a.    Over the given interval, determine when the object is moving in the positive direction and when it is moving in the negative direction.

  b.    Find the displacement over the given interval.

  c.    Find the distance traveled over the given interval.

  d.    Determine the position function s(t) using the Fundamental Theorem of Calculus (Theorem 6.1). Check your answer by finding the position function using the antiderivative method.

3.     $v\left(t\right)=12t^2-30t+12$, for $0\le t\le 3;s\left(0\right)=1$