A particle starting at the origin moves along the x-axis such that its velocity along the line can be modeled by the function v(t)= 2 - 6t units/sec.What is the exact change in position by the function from t = 0 to t = 1.333333?
A)-2.667 units
B)-5.333 units
C)-4.333 units
D)-6.333 units
E)-6.833 units

Question

Quizplus · Accepted Answer

The change in position of the particle can be found by integrating the velocity function over the given time interval. The velocity function is v(t) = 2 - 6t. Integrating this from t = 0 to t = 1.333333 gives the displacement:∫(2 - 6t) dt from 0 to 1.333333 = [2t - 3t^2] from 0 to 1.333333 = (2*1.333333 - 3*(1.333333)^2) - (2*0 - 3*0^2) = 2.666666 - 5.333332 = -2.666666 ≈ -2.667 units.

A Particle Starting at the Origin Moves Along the X-Axis