Physics Fundamentals
Physics Fundamentals
2nd Edition
ISBN: 9780971313453
Author: Vincent P. Coletta
Publisher: PHYSICS CURRICULUM+INSTRUCT.INC.
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Chapter 1, Problem 15P
To determine

The average speed over the different time intervals.

Expert Solution & Answer
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Explanation of Solution

Given:

The three intervals of the motion is 1.0×101s , 1.0×102s and 1.0×103s .

The value of constant c is 1.0m/s3 and initial time is 1.0000 s .

Formula Used:

Speed is the distance covered in unit time by an object. Instantaneous speed is the speed of object at any instant.

Write the expression for final time.

  t=t+Δt ...... (I)

Here, t is the initial time, Δt is the time interval and t is the final interval.

Write the expression for speed of an object for time interval.

  v=sstt

Here, s is the final distance, s is the final speed and v is the speed of object.

Substitute ct3 for s and ct3 for s in above expression.

  v=c( t 3t3)tt ...... (II)

Here, c is the constant given.

Write the expression for instantaneous speed.

  vi=dsdt

Here, vi is the instantaneous speed, ds is the small change in displacement and dt is the small change in time.

Substitute ct3 for s in above expressionand simplify.

  vi=3ct2 ...... (III)

Calculation:

For first time interval:

Substitute 1.0×101s for Δt1 and 1.0000 s for t in equation (I).

  t1=1.0000 s+0.1000s=1.1000s

Substitute 1.1000s for t1 and 1.0000 s for t in equation (II).

  v1=( 1.0m/ s 3 )( ( 1.1000s ) 3 ( 1.0000s ) 3 )( 1.1000s)( 1.0000s)=3.3100m/s

For second time interval:

Substitute 1.0×102s for Δt2 and 1.0000 s for t in equation (I).

  t2=1.0000 s+0.0100s=1.0100s

Substitute 1.0100s for t2 and 1.0000 s for t in equation (II).

  v2=( 1.0m/ s 3 )( ( 1.0100s ) 3 ( 1.0000s ) 3 )( 1.0100s)( 1.0000s)=3.0301m/s

For third time interval:

Substitute 1.0×103s for Δt3 and 1.0000 s for t in equation (I).

  t2=1.0000 s+0.0010s=1.0010s

Substitute 1.0010s for t3 and 1.0000 s for t in equation (II).

  v3=( 1.0m/ s 3 )( ( 1.0010s ) 3 ( 1.0000s ) 3 )( 1.0010s)( 1.0000s)=3.0030m/s

Substitute 1.0m/s3 for c and 1.0000 s for t in equation (III).

  vi=3(1.0m/ s 3)(1.0000 s)2=3m/s

Conclusion:

Thus, the average speed in given three intervals is 3.3100m/s , 3.0301m/s and 3.0030m/s ; the instantaneous speed is 3m/s .

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