Question

A particle moving along x-axis has velocity v(t) = sin(4t) at time t. If the particle is at x=4 when t=0, determine the position of the particle when t=pi/2.

Answer 1

v(t) = ds/dt, so
s(t) = -1/4 cos(4t) + C
s(0) = -1/4 + C = 4, so C = 17/4
s(π/2) = -1/4 cos(π/2) + 17/4 = 17/4

Answer 2

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