Exercise 10

Suppose that the velocity of a moving object is given by $v(t) = t(t-1)(t-3)$, measured in feet per second, and that this function is valid for $0 \le t \le 4$.

1. Write an expression involving definite integrals whose value is the total change in position of the object on the interval $[0,4]$.

2. Use appropriate technology (such as an applet) to compute Riemann sums to estimate the object's total change in position on $[0,4]$. Work to ensure that your estimate is accurate to two decimal places, and explain how you know this to be the case.

3. Write an expression involving definite integrals whose value is the total distance traveled by the object on $[0,4]$.

4. Use appropriate technology to compute Riemann sums to estimate the object's total distance travelled on $[0,4]$. Work to ensure that your estimate is accurate to two decimal places, and explain how you know this to be the case.

5. What is the object's average velocity on $[0,4]$, accurate to two decimal places?