Solved: A particle, initially at rest, moves along the -axis such that its acceleration

Chapter 5, Problem 64

(choose chapter or problem)

In Exercises 61-64, consider a particle moving along the x-axis where \(x(t)\) is the position of the particle at time \(t, x^{\prime}(t)\) is its velocity, and \(x^{\prime \prime}(t)\) is its acceleration.

A particle, initially at rest, moves along the x-axis such that its acceleration at time \(t>0\) is given by \(a(t)=\cos t\). At the time t=0, its position is x=3.

(a) Find the velocity and position functions for the particle.

(b) Find the values of t for which the particle is at rest.

Text Transcription:

x(t)

t, x^{\prime}(t)

x^{\prime \prime}(t)

t>0

a(t)=\cos t