   Chapter 2.R, Problem 1E

Chapter
Section
Textbook Problem

# The displacement (in meters) of an object moving in a straight line is given by s = 1 + 2 t + 1 4 t 2 , where t is measured in seconds.(a) Find the average velocity over each time period.(i) [ 1 , 3 ] (ii) [ 1 , 2 ] (iii) [ 1 , 1.5 ] (iv) [ 1 , 1.1 ] (b) Find the instantaneous velocity when t = 1 .

To determine

(a)

To find:Average velocity over given interval.

Explanation

1) Formula:

average velocity=sb-s(a)b-a

2) Given:

s=1+2t+14t2

3) Calculation:

(i) [1,3]

average velocity=s3-s13-1

=1+2*3+1432-1+2*1+14122

=374-1342

=248

=3m/s

(ii) [1,2]

average velocity=s2-s12-1=s2-s1

=1+2*2+1422-1+2*1+1412

=6-134

=114 m/s or 2

To determine

(b)

To find:Instantaneous velocity at t=1.

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