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(t) = 0 at t=0 and v(t)=100 ft/s at t=4 s. 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 (? t = 10?5 = 2 s).

(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 ? x = ?₀¹⁰ v(t) dt.

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