Question

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

Name: a particle initially at rest moves along the x axis such that its acceleration at time t 0 is given by at sint at the time t 0 its position is x 3 a find the velocity and position functions 74492
Uploaded: 2023-07-10T05:40:08-08:00
Duration: 3 min 50 s
Channel: Khushbu Rani
Description: a particle initially at rest moves along the x axis such that its acceleration at time t 0 is given by at sint at the time t 0 its position is x 3 a find the velocity and position functions 74492

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

Added by Jay M.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Khushbu Rani

07/10/2023

Step 1

First, we need to find the velocity function by integrating the acceleration function: v(t) = ∫a(t) dt = ∫(-sin(t)) dt = cos(t) + C To find the constant C, we know that the particle is initially at rest, which means v(0) = 0: 0 = cos(0) + C C = -1 So the Show more…

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