# Theaverage velocity over given time period. ### Single Variable Calculus: Concepts...

4th Edition
James Stewart
Publisher: Cengage Learning
ISBN: 9781337687805 ### Single Variable Calculus: Concepts...

4th Edition
James Stewart
Publisher: Cengage Learning
ISBN: 9781337687805

#### Solutions

Chapter 2, Problem 27RE

(a)

To determine

## To find:Theaverage velocity over given time period.

Expert Solution

The average velocity over given time period is calculated.

### Explanation of Solution

Given information:

The displacement is given by s=1+2t+14t2 .

Calculation:

(i) Calculate average velocity in [1,3] .

V=s(3)s(1)31=(1+2(3)+14(3)2)(1+2(1)+14(1)2)2=1+6+9412142=62=3m/sec

(ii) Calculate average velocity in [1,2] .

V=s(2)s(1)21=(1+2(2)+14(2)2)(1+2(1)+14(1)2)1=1+4+1134=114=2.75m/sec

(iii) Calculate average velocity in [1,1.5] .

V=s(1.5)s(1)1.51=(1+2(1.5)+14(1.5)2)(1+2(1)+14(1)2)0.5=(1+3+0.5625)(1+2+14)0.5=(4.5625)1340.5=2.625m/sec

(iv) Calculate average velocity in [1,1.1] .

V=s(1.1)s(1)1.11=(1+2(1.1)+14(1.1)2)(1+2(1)+14(1)2)0.1=(1+2.2+0.3025)(3+14)0.1=(3.3025)1340.1=2.525m/sec

Therefore, the average velocity over given time period is calculated.

(b)

To determine

### To find:The instantaneous velocity when t=1 .

Expert Solution

The instantaneous velocity at t=1 is 52m/sec .

### Explanation of Solution

Given information:

The displacement is given by s=1+2t+14t2 .

Calculation:

Calculate instantaneous velocity at t=1 .

V(1)=limh0s(1+h)s(1)h=limh01+2(1+h)+14(1+h)21214h=limh02h+12h+h2h=limh0h(2+12+h)h

=2+12+0=52m/sec

Therefore, the instantaneous velocity at t=1 is 52m/sec .

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