A rigid body with a mass of 2 kg moves along a line due to a force that produces a position function x(t) = 4t², where x is measured in meters and t is measured in seconds. Find the work done during the first 5 s in two ways.

a. Note that x"(t) = 8; then use Newton’s second law (F = ma = mx"(t)) to evaluate the work integral where x₀ and x_f are the initial and final positions, respectively.

b. Change variables in the work integral and integrate with respect to t. Be sure your answer agrees with part (a).

Transcribed Image Text:

F(x) dx. Xf