A particle moves along the x-axis with velocity v(t) = sin (πt) meters/sec.

Question

A particle moves along the -axis with velocity  meters/sec.

(Positive velocity corresponds to movement to the right, and negative velocity- movement to the left.)

Find the position of the particle (on the -axis) at time seconds, given that .

s(1.6) = _____

Round answer to 4 decimal places.

Answer 1

We calculate displacement (change in position over a finite time interval) by integrating the velocity function.

We should note that we are given an initial position, s(0) = .8 . So, we calculate the position when t = 1.6 by adding the displacement on the time interval 0 ≤ t ≤ 1.6 to the starting position of .8:

s(1.6) = .8 + ∫₀^1.6 sin(πt)dt