Find the displacement of a particle if v(t) = cos t; .
A) -1
B) 0
C) 2
E) $\pi$

Question

Find the displacement of a particle if v(t) = cos t;  .
A) -1 
B) 0 
C) 2 
E) $\pi$

Quizplus · Accepted Answer

The displacement function can be found by taking the integral of the velocity function.

∫v(t)dt = ∫cos(t)dt = sin(t) + C

Since we don't have enough information to determine the constant of integration, we can simply use the initial condition that when t = 0, the displacement is 0.

sin(0) + C = 0

C = 0

Therefore, the displacement function is:

s(t) = sin(t)

When t = π,

s(π) = sin(π) = 0 - (-1) = 1

When t = 2π,

s(2π) = sin(2π) = 0

The particle has completed one full cycle between t = 0 and t = 2π, and the maximum displacement is 1 in the negative direction. Therefore, the answer is A) -1.

Find the Displacement of a Particle If V(t) = Cos π\piπ

Find the Displacement of a Particle If V(t) = Cos $\pi$