Problem

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Problem 68 Hard Difficulty

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

Answer

$$
v(t)=\sin (t) \text { and } x(t)=-\cos (t)+4
$$

Topics

Integrals

Integration

Book Cover for Calculus of a Singl…

Calculus of a Single Variable

Chapter 4

Integration

Section 1

Antiderivatives and Indefinite Integration

Discussion

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Video Transcript

So you know that the acceleration and turn to and Cho Santee you know that it starts from rest, so and 00 we now go to your zero The position of time. Zero three. Yeah. So first rule I have to 18. That's the rule. Cosette. Teo signed Too close inconstancy. This is No. This was a colossal time to we know that the velocity A time cereal which happens to me cereal A sequel signs, you know, close. See, which was just see? So that tells us two It's just fine. Two. Now, your team, which is a position of time, Tio is the rule. Yeah, Team two, which is the integral sign? No, which is negative. Kosaka two close some constant of integration was calling d What? Another three is equal to zero physical too Negative co signed here. Clos de Dozens. No, this is negative. One plus two that tells us that Big Siegel for yeah, in the tunes you have to Yeah, lto plus four. Oh, that makes sense.

Allan H.

University of Delaware

Topics

Integrals

Integration

Book Cover for Calculus of a Singl…

Calculus of a Single Variable

Chapter 4

Integration

Section 1

Antiderivatives and Indefinite Integration

Top Calculus 1 / AB Educators

GH

Grace H.

Numerade Educator

Catherine R.

Missouri State University

Heather Z.

Oregon State University

Kristen K.

University of Michigan - Ann Arbor