   Chapter 4.9, Problem 61E ### Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343

#### Solutions

Chapter
Section ### Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343
Textbook Problem

# A particle is moving with the given data. Find the position of the particle.a(t) = 2t + 1, s(0) = 3, v(0) = −2

To determine

To find: The position of particle.

Explanation

Given data:

a(t)=2t+1 , v(0)=2 and s(0)=3 .

Formula Used:

Write the expression for acceleration function a(t) .

a(t)=v(t) (1)

Here,

v(t) is first derivative of velocity function v(t) .

Write the expression for velocity function v(t) .

v(t)=s(t) (2)

Here,

s(t) is first derivative of position function s(t) .

Calculation:

Antiderivative of t2 is 13t3 , t is 12t2 and 1 is t .

Substitute 2t+1 for a(t) in equation (1).

v(t)=2t+1

Antiderivate the expression with respect to t,

v(t)=2(t22)+t+C

v(t)=t2+t+C (3)

Here,

C is arbitrary constant.

Substitute 0 for t in equation (3).

v(0)=02+0+C=C

Substitute –2 for v(0)

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