The average velocity over the time interval t = 0.0 s to t = 10.0 s .

Question

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Answer 1

Question

Chapter 2, Problem 53P

(a)

To determine

The average velocity over the time interval $t=0.0 s$ to $t=10.0 s$ .

(a)

Expert Solution

Answer to Problem 53P

The average velocity over the time interval $t=0.0 s$ to $t=10.0 s$ , is $3.0 m/s_$ .

Explanation of Solution

Write the expression for average velocity.

$vavg=ΔxΔt$ (I)

Conclusion:

Substitute, $30 m−0 m$ for $Δx$ , and $10.0 s−0.0 s$ for $Δt$ in equation (I) to find the average velocity from $t=0.0 s$ to $t=10.0 s$ .

$vavg=30 m−0 m10.0 s−0 s=3.0 m/s$

Therefore, the average velocity over the time interval $t=0.0 s$ to $t=10.0 s$ , is $3.0 m/s_$ .

(b)

To determine

The average velocity over the time interval $t=0.0 s$ to $t=5.0 s$ .

(b)

Expert Solution

Answer to Problem 53P

The average velocity over the time interval $t=0.0 s$ to $t=5.0 s$ is $4.5 m/s_$ .

Explanation of Solution

Use equation (I) to find the answer.

Conclusion:

Substitute, $22.5 m−0 m$ for $Δx$ , and $5.0 s−0.0 s$ for $Δt$ in equation (I) to find the average velocity from $t=0.0 s$ to $t=5.0 s$ .

$vavg=22.5 m−0 m5.0 s−0 s=4.5 m/s$

Therefore, the average velocity over the time interval $t=0.0 s$ to $t=5.0 s$ is $4.5 m/s_$ .

(c)

To determine

The average velocity between $t=5.0 s$ and $t=10.0 s$ .

(c)

Expert Solution

Answer to Problem 53P

The average velocity between $t=5.0 s$ and $t=10.0 s$ is $1.5 m/s_$ .

Explanation of Solution

Use equation (I) to find the answer.

Conclusion:

Substitute, $30 m−22.5 m$ for $Δx$ , and $10.0 s−5.0 s$ for $Δt$ in equation (I) to find the average velocity from $t=5.0 s$ to $t=10.0 s$ .

$vavg=30 m−22.5 m10.0 s−5.0 s=1.5 m/s$

Therefore, the average velocity between $t=5.0 s$ and $t=10.0 s$ is $1.5 m/s_$ .

(d)

To determine

The relation of answers in part (a), (b), and (c).

(d)

Expert Solution

Answer to Problem 53P

The relation is average of answers in part (b), and (c) is answer in part (a).

Explanation of Solution

The total average velocity over the time interval $t=0.0 s$ to $t=10.0 s$ must be equal to the average of the individual average velocities for the time intervals $t=0.0 s$ to $t=5.0 s$ and $t=5.0 s$ to $t=10.0 s$ .

Write the expression for the average velocity.

$vavg,a=vavg,b+vavg,c2$ (II)

Conclusion:

Substitute, $4.5 m/s$ for $vavg,b$ , $1.5 m/s$ for $vavg,c$ in equation (II).

$vavg,a=4.5 m/s+1.5 m/s2=3.0 m/s$

Therefore, the relation is average of answers in part (b), and (c) is answer in part (a).

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Answer 2

Question

Chapter 2, Problem 53P

(a)

To determine

The average velocity over the time interval $t=0.0 s$ to $t=10.0 s$ .

(a)

Expert Solution

Answer to Problem 53P

The average velocity over the time interval $t=0.0 s$ to $t=10.0 s$ , is $3.0 m/s_$ .

Explanation of Solution

Write the expression for average velocity.

$vavg=ΔxΔt$ (I)

Conclusion:

Substitute, $30 m−0 m$ for $Δx$ , and $10.0 s−0.0 s$ for $Δt$ in equation (I) to find the average velocity from $t=0.0 s$ to $t=10.0 s$ .

$vavg=30 m−0 m10.0 s−0 s=3.0 m/s$

Therefore, the average velocity over the time interval $t=0.0 s$ to $t=10.0 s$ , is $3.0 m/s_$ .

(b)

To determine

The average velocity over the time interval $t=0.0 s$ to $t=5.0 s$ .

(b)

Expert Solution

Answer to Problem 53P

The average velocity over the time interval $t=0.0 s$ to $t=5.0 s$ is $4.5 m/s_$ .

Explanation of Solution

Use equation (I) to find the answer.

Conclusion:

Substitute, $22.5 m−0 m$ for $Δx$ , and $5.0 s−0.0 s$ for $Δt$ in equation (I) to find the average velocity from $t=0.0 s$ to $t=5.0 s$ .

$vavg=22.5 m−0 m5.0 s−0 s=4.5 m/s$

Therefore, the average velocity over the time interval $t=0.0 s$ to $t=5.0 s$ is $4.5 m/s_$ .

(c)

To determine

The average velocity between $t=5.0 s$ and $t=10.0 s$ .

(c)

Expert Solution

Answer to Problem 53P

The average velocity between $t=5.0 s$ and $t=10.0 s$ is $1.5 m/s_$ .

Explanation of Solution

Use equation (I) to find the answer.

Conclusion:

Substitute, $30 m−22.5 m$ for $Δx$ , and $10.0 s−5.0 s$ for $Δt$ in equation (I) to find the average velocity from $t=5.0 s$ to $t=10.0 s$ .

$vavg=30 m−22.5 m10.0 s−5.0 s=1.5 m/s$

Therefore, the average velocity between $t=5.0 s$ and $t=10.0 s$ is $1.5 m/s_$ .

(d)

To determine

The relation of answers in part (a), (b), and (c).

(d)

Expert Solution

Answer to Problem 53P

The relation is average of answers in part (b), and (c) is answer in part (a).

Explanation of Solution

The total average velocity over the time interval $t=0.0 s$ to $t=10.0 s$ must be equal to the average of the individual average velocities for the time intervals $t=0.0 s$ to $t=5.0 s$ and $t=5.0 s$ to $t=10.0 s$ .

Write the expression for the average velocity.

$vavg,a=vavg,b+vavg,c2$ (II)

Conclusion:

Substitute, $4.5 m/s$ for $vavg,b$ , $1.5 m/s$ for $vavg,c$ in equation (II).

$vavg,a=4.5 m/s+1.5 m/s2=3.0 m/s$

Therefore, the relation is average of answers in part (b), and (c) is answer in part (a).

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Answer 3

Question

Chapter 2, Problem 53P

(a)

To determine

The average velocity over the time interval $t=0.0 s$ to $t=10.0 s$ .

(a)

Expert Solution

Answer to Problem 53P

The average velocity over the time interval $t=0.0 s$ to $t=10.0 s$ , is $3.0 m/s_$ .

Explanation of Solution

Write the expression for average velocity.

$vavg=ΔxΔt$ (I)

Conclusion:

Substitute, $30 m−0 m$ for $Δx$ , and $10.0 s−0.0 s$ for $Δt$ in equation (I) to find the average velocity from $t=0.0 s$ to $t=10.0 s$ .

$vavg=30 m−0 m10.0 s−0 s=3.0 m/s$

Therefore, the average velocity over the time interval $t=0.0 s$ to $t=10.0 s$ , is $3.0 m/s_$ .

(b)

To determine

The average velocity over the time interval $t=0.0 s$ to $t=5.0 s$ .

(b)

Expert Solution

Answer to Problem 53P

The average velocity over the time interval $t=0.0 s$ to $t=5.0 s$ is $4.5 m/s_$ .

Explanation of Solution

Use equation (I) to find the answer.

Conclusion:

Substitute, $22.5 m−0 m$ for $Δx$ , and $5.0 s−0.0 s$ for $Δt$ in equation (I) to find the average velocity from $t=0.0 s$ to $t=5.0 s$ .

$vavg=22.5 m−0 m5.0 s−0 s=4.5 m/s$

Therefore, the average velocity over the time interval $t=0.0 s$ to $t=5.0 s$ is $4.5 m/s_$ .

(c)

To determine

The average velocity between $t=5.0 s$ and $t=10.0 s$ .

(c)

Expert Solution

Answer to Problem 53P

The average velocity between $t=5.0 s$ and $t=10.0 s$ is $1.5 m/s_$ .

Explanation of Solution

Use equation (I) to find the answer.

Conclusion:

Substitute, $30 m−22.5 m$ for $Δx$ , and $10.0 s−5.0 s$ for $Δt$ in equation (I) to find the average velocity from $t=5.0 s$ to $t=10.0 s$ .

$vavg=30 m−22.5 m10.0 s−5.0 s=1.5 m/s$

Therefore, the average velocity between $t=5.0 s$ and $t=10.0 s$ is $1.5 m/s_$ .

(d)

To determine

The relation of answers in part (a), (b), and (c).

(d)

Expert Solution

Answer to Problem 53P

The relation is average of answers in part (b), and (c) is answer in part (a).

Explanation of Solution

The total average velocity over the time interval $t=0.0 s$ to $t=10.0 s$ must be equal to the average of the individual average velocities for the time intervals $t=0.0 s$ to $t=5.0 s$ and $t=5.0 s$ to $t=10.0 s$ .

Write the expression for the average velocity.

$vavg,a=vavg,b+vavg,c2$ (II)

Conclusion:

Substitute, $4.5 m/s$ for $vavg,b$ , $1.5 m/s$ for $vavg,c$ in equation (II).

$vavg,a=4.5 m/s+1.5 m/s2=3.0 m/s$

Therefore, the relation is average of answers in part (b), and (c) is answer in part (a).

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Answer 4

Question

Chapter 2, Problem 53P

(a)

To determine

The average velocity over the time interval $t=0.0 s$ to $t=10.0 s$ .

(a)

Expert Solution

Answer to Problem 53P

The average velocity over the time interval $t=0.0 s$ to $t=10.0 s$ , is $3.0 m/s_$ .

Explanation of Solution

Write the expression for average velocity.

$vavg=ΔxΔt$ (I)

Conclusion:

Substitute, $30 m−0 m$ for $Δx$ , and $10.0 s−0.0 s$ for $Δt$ in equation (I) to find the average velocity from $t=0.0 s$ to $t=10.0 s$ .

$vavg=30 m−0 m10.0 s−0 s=3.0 m/s$

Therefore, the average velocity over the time interval $t=0.0 s$ to $t=10.0 s$ , is $3.0 m/s_$ .

(b)

To determine

The average velocity over the time interval $t=0.0 s$ to $t=5.0 s$ .

(b)

Expert Solution

Answer to Problem 53P

The average velocity over the time interval $t=0.0 s$ to $t=5.0 s$ is $4.5 m/s_$ .

Explanation of Solution

Use equation (I) to find the answer.

Conclusion:

Substitute, $22.5 m−0 m$ for $Δx$ , and $5.0 s−0.0 s$ for $Δt$ in equation (I) to find the average velocity from $t=0.0 s$ to $t=5.0 s$ .

$vavg=22.5 m−0 m5.0 s−0 s=4.5 m/s$

Therefore, the average velocity over the time interval $t=0.0 s$ to $t=5.0 s$ is $4.5 m/s_$ .

(c)

To determine

The average velocity between $t=5.0 s$ and $t=10.0 s$ .

(c)

Expert Solution

Answer to Problem 53P

The average velocity between $t=5.0 s$ and $t=10.0 s$ is $1.5 m/s_$ .

Explanation of Solution

Use equation (I) to find the answer.

Conclusion:

Substitute, $30 m−22.5 m$ for $Δx$ , and $10.0 s−5.0 s$ for $Δt$ in equation (I) to find the average velocity from $t=5.0 s$ to $t=10.0 s$ .

$vavg=30 m−22.5 m10.0 s−5.0 s=1.5 m/s$

Therefore, the average velocity between $t=5.0 s$ and $t=10.0 s$ is $1.5 m/s_$ .

(d)

To determine

The relation of answers in part (a), (b), and (c).

(d)

Expert Solution

Answer to Problem 53P

The relation is average of answers in part (b), and (c) is answer in part (a).

Explanation of Solution

The total average velocity over the time interval $t=0.0 s$ to $t=10.0 s$ must be equal to the average of the individual average velocities for the time intervals $t=0.0 s$ to $t=5.0 s$ and $t=5.0 s$ to $t=10.0 s$ .

Write the expression for the average velocity.

$vavg,a=vavg,b+vavg,c2$ (II)

Conclusion:

Substitute, $4.5 m/s$ for $vavg,b$ , $1.5 m/s$ for $vavg,c$ in equation (II).

$vavg,a=4.5 m/s+1.5 m/s2=3.0 m/s$

Therefore, the relation is average of answers in part (b), and (c) is answer in part (a).

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Answer 5

Chapter 2, Problem 53P

(a)

To determine

The average velocity over the time interval $t=0.0 s$ to $t=10.0 s$ .

(a)

Expert Solution

Answer to Problem 53P

The average velocity over the time interval $t=0.0 s$ to $t=10.0 s$ , is $3.0 m/s_$ .

Explanation of Solution

Write the expression for average velocity.

$vavg=ΔxΔt$ (I)

Conclusion:

Substitute, $30 m−0 m$ for $Δx$ , and $10.0 s−0.0 s$ for $Δt$ in equation (I) to find the average velocity from $t=0.0 s$ to $t=10.0 s$ .

$vavg=30 m−0 m10.0 s−0 s=3.0 m/s$

Therefore, the average velocity over the time interval $t=0.0 s$ to $t=10.0 s$ , is $3.0 m/s_$ .

(b)

To determine

The average velocity over the time interval $t=0.0 s$ to $t=5.0 s$ .

(b)

Expert Solution

Answer to Problem 53P

The average velocity over the time interval $t=0.0 s$ to $t=5.0 s$ is $4.5 m/s_$ .

Explanation of Solution

Use equation (I) to find the answer.

Conclusion:

Substitute, $22.5 m−0 m$ for $Δx$ , and $5.0 s−0.0 s$ for $Δt$ in equation (I) to find the average velocity from $t=0.0 s$ to $t=5.0 s$ .

$vavg=22.5 m−0 m5.0 s−0 s=4.5 m/s$

Therefore, the average velocity over the time interval $t=0.0 s$ to $t=5.0 s$ is $4.5 m/s_$ .

(c)

To determine

The average velocity between $t=5.0 s$ and $t=10.0 s$ .

(c)

Expert Solution

Answer to Problem 53P

The average velocity between $t=5.0 s$ and $t=10.0 s$ is $1.5 m/s_$ .

Explanation of Solution

Use equation (I) to find the answer.

Conclusion:

Substitute, $30 m−22.5 m$ for $Δx$ , and $10.0 s−5.0 s$ for $Δt$ in equation (I) to find the average velocity from $t=5.0 s$ to $t=10.0 s$ .

$vavg=30 m−22.5 m10.0 s−5.0 s=1.5 m/s$

Therefore, the average velocity between $t=5.0 s$ and $t=10.0 s$ is $1.5 m/s_$ .

(d)

To determine

The relation of answers in part (a), (b), and (c).

(d)

Expert Solution

Answer to Problem 53P

The relation is average of answers in part (b), and (c) is answer in part (a).

Explanation of Solution

The total average velocity over the time interval $t=0.0 s$ to $t=10.0 s$ must be equal to the average of the individual average velocities for the time intervals $t=0.0 s$ to $t=5.0 s$ and $t=5.0 s$ to $t=10.0 s$ .

Write the expression for the average velocity.

$vavg,a=vavg,b+vavg,c2$ (II)

Conclusion:

Substitute, $4.5 m/s$ for $vavg,b$ , $1.5 m/s$ for $vavg,c$ in equation (II).

$vavg,a=4.5 m/s+1.5 m/s2=3.0 m/s$

Therefore, the relation is average of answers in part (b), and (c) is answer in part (a).

Answer 6

Chapter 2, Problem 53P

(a)

To determine

The average velocity over the time interval $t=0.0 s$ to $t=10.0 s$ .

(a)

Expert Solution

Answer to Problem 53P

The average velocity over the time interval $t=0.0 s$ to $t=10.0 s$ , is $3.0 m/s_$ .

Explanation of Solution

Write the expression for average velocity.

$vavg=ΔxΔt$ (I)

Conclusion:

Substitute, $30 m−0 m$ for $Δx$ , and $10.0 s−0.0 s$ for $Δt$ in equation (I) to find the average velocity from $t=0.0 s$ to $t=10.0 s$ .

$vavg=30 m−0 m10.0 s−0 s=3.0 m/s$

Therefore, the average velocity over the time interval $t=0.0 s$ to $t=10.0 s$ , is $3.0 m/s_$ .

Answer 7

Chapter 2, Problem 53P

(a)

To determine

The average velocity over the time interval $t=0.0 s$ to $t=10.0 s$ .

Answer 8

(a)

Expert Solution

Answer to Problem 53P

The average velocity over the time interval $t=0.0 s$ to $t=10.0 s$ , is $3.0 m/s_$ .

Answer 9

(a)

Expert Solution

Answer 10

(a)

Expert Solution

Answer 11

Expert Solution

Answer 12

Explanation of Solution

Write the expression for average velocity.

$vavg=ΔxΔt$ (I)

Conclusion:

Substitute, $30 m−0 m$ for $Δx$ , and $10.0 s−0.0 s$ for $Δt$ in equation (I) to find the average velocity from $t=0.0 s$ to $t=10.0 s$ .

$vavg=30 m−0 m10.0 s−0 s=3.0 m/s$

Therefore, the average velocity over the time interval $t=0.0 s$ to $t=10.0 s$ , is $3.0 m/s_$ .

Answer 13

(b)

To determine

The average velocity over the time interval $t=0.0 s$ to $t=5.0 s$ .

(b)

Expert Solution

Answer to Problem 53P

The average velocity over the time interval $t=0.0 s$ to $t=5.0 s$ is $4.5 m/s_$ .

Explanation of Solution

Use equation (I) to find the answer.

Conclusion:

Substitute, $22.5 m−0 m$ for $Δx$ , and $5.0 s−0.0 s$ for $Δt$ in equation (I) to find the average velocity from $t=0.0 s$ to $t=5.0 s$ .

$vavg=22.5 m−0 m5.0 s−0 s=4.5 m/s$

Therefore, the average velocity over the time interval $t=0.0 s$ to $t=5.0 s$ is $4.5 m/s_$ .

Answer 14

(b)

To determine

The average velocity over the time interval $t=0.0 s$ to $t=5.0 s$ .

Answer 15

(b)

Expert Solution

Answer to Problem 53P

The average velocity over the time interval $t=0.0 s$ to $t=5.0 s$ is $4.5 m/s_$ .

Answer 16

(b)

Expert Solution

Answer 17

(b)

Expert Solution

Answer 18

Expert Solution

Answer 19

Explanation of Solution

Use equation (I) to find the answer.

Conclusion:

Substitute, $22.5 m−0 m$ for $Δx$ , and $5.0 s−0.0 s$ for $Δt$ in equation (I) to find the average velocity from $t=0.0 s$ to $t=5.0 s$ .

$vavg=22.5 m−0 m5.0 s−0 s=4.5 m/s$

Therefore, the average velocity over the time interval $t=0.0 s$ to $t=5.0 s$ is $4.5 m/s_$ .

Answer 20

(c)

To determine

The average velocity between $t=5.0 s$ and $t=10.0 s$ .

(c)

Expert Solution

Answer to Problem 53P

The average velocity between $t=5.0 s$ and $t=10.0 s$ is $1.5 m/s_$ .

Explanation of Solution

Use equation (I) to find the answer.

Conclusion:

Substitute, $30 m−22.5 m$ for $Δx$ , and $10.0 s−5.0 s$ for $Δt$ in equation (I) to find the average velocity from $t=5.0 s$ to $t=10.0 s$ .

$vavg=30 m−22.5 m10.0 s−5.0 s=1.5 m/s$

Therefore, the average velocity between $t=5.0 s$ and $t=10.0 s$ is $1.5 m/s_$ .

Answer 21

(c)

To determine

The average velocity between $t=5.0 s$ and $t=10.0 s$ .

Answer 22

(c)

Expert Solution

Answer to Problem 53P

The average velocity between $t=5.0 s$ and $t=10.0 s$ is $1.5 m/s_$ .

Answer 23

(c)

Expert Solution

Answer 24

(c)

Expert Solution

Answer 25

Expert Solution

Answer 26

Explanation of Solution

Use equation (I) to find the answer.

Conclusion:

Substitute, $30 m−22.5 m$ for $Δx$ , and $10.0 s−5.0 s$ for $Δt$ in equation (I) to find the average velocity from $t=5.0 s$ to $t=10.0 s$ .

$vavg=30 m−22.5 m10.0 s−5.0 s=1.5 m/s$

Therefore, the average velocity between $t=5.0 s$ and $t=10.0 s$ is $1.5 m/s_$ .

Answer 27

(d)

To determine

The relation of answers in part (a), (b), and (c).

(d)

Expert Solution

Answer to Problem 53P

The relation is average of answers in part (b), and (c) is answer in part (a).

Explanation of Solution

The total average velocity over the time interval $t=0.0 s$ to $t=10.0 s$ must be equal to the average of the individual average velocities for the time intervals $t=0.0 s$ to $t=5.0 s$ and $t=5.0 s$ to $t=10.0 s$ .

Write the expression for the average velocity.

$vavg,a=vavg,b+vavg,c2$ (II)

Conclusion:

Substitute, $4.5 m/s$ for $vavg,b$ , $1.5 m/s$ for $vavg,c$ in equation (II).

$vavg,a=4.5 m/s+1.5 m/s2=3.0 m/s$

Therefore, the relation is average of answers in part (b), and (c) is answer in part (a).

Answer 28

(d)

To determine

The relation of answers in part (a), (b), and (c).

Answer 29

(d)

Expert Solution

Answer to Problem 53P

The relation is average of answers in part (b), and (c) is answer in part (a).

Answer 30

(d)

Expert Solution

Answer 31

(d)

Expert Solution

Answer 32

Expert Solution

Answer 33

Explanation of Solution

The total average velocity over the time interval $t=0.0 s$ to $t=10.0 s$ must be equal to the average of the individual average velocities for the time intervals $t=0.0 s$ to $t=5.0 s$ and $t=5.0 s$ to $t=10.0 s$ .