A Particle Moves Along A Line With Velocity V T Cos 2 T For 0 T 2

A particle moves along a line with velocity v(t) = cos(6πt) for 0 ≤ t ≤ 4.

a) Find the displacement.

b) Find the distance traveled

Solution

a)Displacement S = ∫02cos(2πt)dt = 1/2πsin(2πt)02 = 1/2π(sin(4π) – sin(0)) = 0;

b) Distance D = ∫02abs(cos(2πt))dt = 8∫01/4cos(2πt)dt = 8/2πsin(2πt)01/4 =4/π(sin(π/2) – sin(0)) = 4/π ≈ 1.273