The relationship between the velocity of a body moving along the x axis and time is given by v = 2t³ + 2t,where the units are SI units.The total distance the body travels between the times t = 2 s and t = 4 s is A)132 m B)144 m C)136 m D)120 m E)156 m

Question

Quizplus · Accepted Answer

To find the total distance traveled, integrate the velocity function v = 2t^3 + 2t with respect to time from t = 2 to t = 4. The integral of v is (1/2)(2t^4) + (1/2)(2t^2) = (1/2)(2t^4 + 2t^2). Evaluating this from 2 to 4 gives 132 m.

The Relationship Between the Velocity of a Body Moving Along