   Chapter 3.9, Problem 53E

Chapter
Section
Textbook Problem

# 53-58 A particle is moving with the given data. Find the position of the particle. v ( t ) = sin t − cos t ,    s ( 0 ) = 0

To determine

To find:

The position of the particle s(t)

Explanation

1) Concept:

The position function is an antiderivative of the velocity function.

vt=ddxst

2) Given:

vt=sint-cost,  s0=0.

3) Calculations:

Here, vt=sint-cost

A particle is moving with a velocity of vt=sint-cost and s0=0

Let, s(t) be the position of the particle.

s(t) is an antiderivative of vt.

By using the antiderivative rules,

st=-cost-sint+C

It is given that s0=0

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