Chapter 9, Problem 3P

The velocity of an object as a function of time is shown in Fig. P9.3. The acceleration is constant during the first 4 seconds of motion, so the velocity is a linear function of time with $v\left(t\right)=0$ at $t=0$ and $v\left(t\right)=100\text{ft/s}$ at $t=4s$. The velocity is constant during the last 6 s.

(a) Estimate the total distance covered (the area, A) under the velocity curve using five rectangles of equal width $\left(\Delta t=10/5=2s\right)$.

(b) Now estimate the total distance covered using 10 rectangles of equal width.

(c) Calculate the exact area under the velocity curve; i.e., Find the total distance traveled by evaluating the definite integral $\Delta x={\displaystyle \underset{0}{\overset{l0}{\int }}v\left(t\right)dt}$.

(d) Calculate the exact area by adding the area of the triangle and the area of the rectangle hounded by the velocity curve.