To decide: Whether the given statement is true or false.

Question

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Answer 1

Question

Chapter 26, Problem 1RE

To determine

To decide: Whether the given statement is true or false.

Expert Solution & Answer

Answer to Problem 1RE

The given statement is True_.

Explanation of Solution

Consider the give statement.

Let the initial velocity of an object be v0.

Since the horizontal velocity of an object is 8 m/s2, the velocity along the straight line will be v=v0+8t, where t is time.

Note that, the displacement s in terms of time t is s=∫vdt.

Substitute v=v0+8t in s=∫vdt and simplify for s.

s=∫(v0+8t)dt=v0∫tdt+8∫tdt=v0t+4t2+C

The distance travelled in previous second is obtained by replacing t by t−1 as follows.

s(t−1)=v0(t−1)+4(t−1)2+C=v0t−v0+4t2+4−8t+C

Hence, distance travelled in the second before a given time is obtained as follows.

s(t)−s(t−1)=v0t+4t2+C−(v0t−v0+4t2+4−8t+C)=v0t+4t2+C−v0t+v0−4t2−4+8t−C=v0+8t−4+(v0t−v0t)+(4t2−4t2)+(C−C)=v0+8t−4

The distance travelled in after the second is obtained by replacing t by t+1 as follows.

s(t+1)=v0(t+1)+4(t+1)2+C=v0t+v0+4t2+4+8t+C

Hence, distance travelled in the second after a given time is obtained as follows.

s(t+1)−s(t)=(v0t+v0+4t2+4+8t+C)−(v0t+4t2+C)=v0t+v0+4t2+4+8t+C−v0t−4t2−C=v0+8t+4+(v0t−v0t)+(4t2−4t2)+(C−C)=v0+8t+4

Calculate difference of the above distances.

s(t+1)−s(t)−s(t−1)+s(t)=v0+8t+4−v0−8t+4s(t+1)−s(t−1)=8

Thus, the given statement is True_.

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Last Chance Mine (LCM) purchased a coal deposit for $2,918,300. It estimated it would extract 18,950 tons of coal from the deposit. LCM mined the coal and sold it, reporting gross receipts of $1.24 million, $13 million, and $11 million for years 1 through 3, respectively. During years 1-3, LCM reported net income (loss) from the coal deposit activity in the amount of ($11,400), $550,000, and $502,500, respectively. In years 1-3, LCM extracted 19,950 tons of coal as follows: (1) Tons of Coal 18,950 Depletion (2) Basis (2)(1) Rate $2,918,300 $154.00 Tons Extracted per Year Year 1 4,500 Year 2 8,850 Year 3 6,600 Note: Leave no answer blank. Enter zero if applicable. Enter your answers in dollars and not in millions of dollars. a. What is LCM's cost depletion for years 1, 2, and 3? Cost Depletion Year 1 Year 2 Year 3

Answer 2

Question

Chapter 26, Problem 1RE

To determine

To decide: Whether the given statement is true or false.

Expert Solution & Answer

Answer to Problem 1RE

The given statement is True_.

Explanation of Solution

Consider the give statement.

Let the initial velocity of an object be v0.

Since the horizontal velocity of an object is 8 m/s2, the velocity along the straight line will be v=v0+8t, where t is time.

Note that, the displacement s in terms of time t is s=∫vdt.

Substitute v=v0+8t in s=∫vdt and simplify for s.

s=∫(v0+8t)dt=v0∫tdt+8∫tdt=v0t+4t2+C

The distance travelled in previous second is obtained by replacing t by t−1 as follows.

s(t−1)=v0(t−1)+4(t−1)2+C=v0t−v0+4t2+4−8t+C

Hence, distance travelled in the second before a given time is obtained as follows.

s(t)−s(t−1)=v0t+4t2+C−(v0t−v0+4t2+4−8t+C)=v0t+4t2+C−v0t+v0−4t2−4+8t−C=v0+8t−4+(v0t−v0t)+(4t2−4t2)+(C−C)=v0+8t−4

The distance travelled in after the second is obtained by replacing t by t+1 as follows.

s(t+1)=v0(t+1)+4(t+1)2+C=v0t+v0+4t2+4+8t+C

Hence, distance travelled in the second after a given time is obtained as follows.

s(t+1)−s(t)=(v0t+v0+4t2+4+8t+C)−(v0t+4t2+C)=v0t+v0+4t2+4+8t+C−v0t−4t2−C=v0+8t+4+(v0t−v0t)+(4t2−4t2)+(C−C)=v0+8t+4

Calculate difference of the above distances.

s(t+1)−s(t)−s(t−1)+s(t)=v0+8t+4−v0−8t+4s(t+1)−s(t−1)=8

Thus, the given statement is True_.

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Answer 3

Question

Chapter 26, Problem 1RE

To determine

To decide: Whether the given statement is true or false.

Expert Solution & Answer

Answer to Problem 1RE

The given statement is True_.

Explanation of Solution

Consider the give statement.

Let the initial velocity of an object be v0.

Since the horizontal velocity of an object is 8 m/s2, the velocity along the straight line will be v=v0+8t, where t is time.

Note that, the displacement s in terms of time t is s=∫vdt.

Substitute v=v0+8t in s=∫vdt and simplify for s.

s=∫(v0+8t)dt=v0∫tdt+8∫tdt=v0t+4t2+C

The distance travelled in previous second is obtained by replacing t by t−1 as follows.

s(t−1)=v0(t−1)+4(t−1)2+C=v0t−v0+4t2+4−8t+C

Hence, distance travelled in the second before a given time is obtained as follows.

s(t)−s(t−1)=v0t+4t2+C−(v0t−v0+4t2+4−8t+C)=v0t+4t2+C−v0t+v0−4t2−4+8t−C=v0+8t−4+(v0t−v0t)+(4t2−4t2)+(C−C)=v0+8t−4

The distance travelled in after the second is obtained by replacing t by t+1 as follows.

s(t+1)=v0(t+1)+4(t+1)2+C=v0t+v0+4t2+4+8t+C

Hence, distance travelled in the second after a given time is obtained as follows.

s(t+1)−s(t)=(v0t+v0+4t2+4+8t+C)−(v0t+4t2+C)=v0t+v0+4t2+4+8t+C−v0t−4t2−C=v0+8t+4+(v0t−v0t)+(4t2−4t2)+(C−C)=v0+8t+4

Calculate difference of the above distances.

s(t+1)−s(t)−s(t−1)+s(t)=v0+8t+4−v0−8t+4s(t+1)−s(t−1)=8

Thus, the given statement is True_.

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Answer 4

Question

Chapter 26, Problem 1RE

To determine

To decide: Whether the given statement is true or false.

Expert Solution & Answer

Answer to Problem 1RE

The given statement is True_.

Explanation of Solution

Consider the give statement.

Let the initial velocity of an object be v0.

Since the horizontal velocity of an object is 8 m/s2, the velocity along the straight line will be v=v0+8t, where t is time.

Note that, the displacement s in terms of time t is s=∫vdt.

Substitute v=v0+8t in s=∫vdt and simplify for s.

s=∫(v0+8t)dt=v0∫tdt+8∫tdt=v0t+4t2+C

The distance travelled in previous second is obtained by replacing t by t−1 as follows.

s(t−1)=v0(t−1)+4(t−1)2+C=v0t−v0+4t2+4−8t+C

Hence, distance travelled in the second before a given time is obtained as follows.

s(t)−s(t−1)=v0t+4t2+C−(v0t−v0+4t2+4−8t+C)=v0t+4t2+C−v0t+v0−4t2−4+8t−C=v0+8t−4+(v0t−v0t)+(4t2−4t2)+(C−C)=v0+8t−4

The distance travelled in after the second is obtained by replacing t by t+1 as follows.

s(t+1)=v0(t+1)+4(t+1)2+C=v0t+v0+4t2+4+8t+C

Hence, distance travelled in the second after a given time is obtained as follows.

s(t+1)−s(t)=(v0t+v0+4t2+4+8t+C)−(v0t+4t2+C)=v0t+v0+4t2+4+8t+C−v0t−4t2−C=v0+8t+4+(v0t−v0t)+(4t2−4t2)+(C−C)=v0+8t+4

Calculate difference of the above distances.

s(t+1)−s(t)−s(t−1)+s(t)=v0+8t+4−v0−8t+4s(t+1)−s(t−1)=8

Thus, the given statement is True_.

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Answer 5

Chapter 26, Problem 1RE

To determine

To decide: Whether the given statement is true or false.

Expert Solution & Answer

Answer to Problem 1RE

The given statement is True_.

Explanation of Solution

Consider the give statement.

Let the initial velocity of an object be v0.

Since the horizontal velocity of an object is 8 m/s2, the velocity along the straight line will be v=v0+8t, where t is time.

Note that, the displacement s in terms of time t is s=∫vdt.

Substitute v=v0+8t in s=∫vdt and simplify for s.

s=∫(v0+8t)dt=v0∫tdt+8∫tdt=v0t+4t2+C

The distance travelled in previous second is obtained by replacing t by t−1 as follows.

s(t−1)=v0(t−1)+4(t−1)2+C=v0t−v0+4t2+4−8t+C

Hence, distance travelled in the second before a given time is obtained as follows.

s(t)−s(t−1)=v0t+4t2+C−(v0t−v0+4t2+4−8t+C)=v0t+4t2+C−v0t+v0−4t2−4+8t−C=v0+8t−4+(v0t−v0t)+(4t2−4t2)+(C−C)=v0+8t−4

The distance travelled in after the second is obtained by replacing t by t+1 as follows.

s(t+1)=v0(t+1)+4(t+1)2+C=v0t+v0+4t2+4+8t+C

Hence, distance travelled in the second after a given time is obtained as follows.

s(t+1)−s(t)=(v0t+v0+4t2+4+8t+C)−(v0t+4t2+C)=v0t+v0+4t2+4+8t+C−v0t−4t2−C=v0+8t+4+(v0t−v0t)+(4t2−4t2)+(C−C)=v0+8t+4

Calculate difference of the above distances.

s(t+1)−s(t)−s(t−1)+s(t)=v0+8t+4−v0−8t+4s(t+1)−s(t−1)=8

Thus, the given statement is True_.

Answer 6

Chapter 26, Problem 1RE

To determine

To decide: Whether the given statement is true or false.

Expert Solution & Answer

Answer to Problem 1RE

The given statement is True_.

Explanation of Solution

Consider the give statement.

Let the initial velocity of an object be v0.

Since the horizontal velocity of an object is 8 m/s2, the velocity along the straight line will be v=v0+8t, where t is time.

Note that, the displacement s in terms of time t is s=∫vdt.

Substitute v=v0+8t in s=∫vdt and simplify for s.

s=∫(v0+8t)dt=v0∫tdt+8∫tdt=v0t+4t2+C

The distance travelled in previous second is obtained by replacing t by t−1 as follows.

s(t−1)=v0(t−1)+4(t−1)2+C=v0t−v0+4t2+4−8t+C

Hence, distance travelled in the second before a given time is obtained as follows.

s(t)−s(t−1)=v0t+4t2+C−(v0t−v0+4t2+4−8t+C)=v0t+4t2+C−v0t+v0−4t2−4+8t−C=v0+8t−4+(v0t−v0t)+(4t2−4t2)+(C−C)=v0+8t−4

The distance travelled in after the second is obtained by replacing t by t+1 as follows.

s(t+1)=v0(t+1)+4(t+1)2+C=v0t+v0+4t2+4+8t+C

Hence, distance travelled in the second after a given time is obtained as follows.

s(t+1)−s(t)=(v0t+v0+4t2+4+8t+C)−(v0t+4t2+C)=v0t+v0+4t2+4+8t+C−v0t−4t2−C=v0+8t+4+(v0t−v0t)+(4t2−4t2)+(C−C)=v0+8t+4

Calculate difference of the above distances.

s(t+1)−s(t)−s(t−1)+s(t)=v0+8t+4−v0−8t+4s(t+1)−s(t−1)=8

Thus, the given statement is True_.

Answer 7

Chapter 26, Problem 1RE

To determine

To decide: Whether the given statement is true or false.

Answer 8

Expert Solution & Answer

Answer to Problem 1RE

The given statement is True_.

Answer 9

Expert Solution & Answer

Answer 10

Expert Solution & Answer

Answer 11

Explanation of Solution

Consider the give statement.

Let the initial velocity of an object be v0.

Since the horizontal velocity of an object is 8 m/s2, the velocity along the straight line will be v=v0+8t, where t is time.

Note that, the displacement s in terms of time t is s=∫vdt.

Substitute v=v0+8t in s=∫vdt and simplify for s.

s=∫(v0+8t)dt=v0∫tdt+8∫tdt=v0t+4t2+C

The distance travelled in previous second is obtained by replacing t by t−1 as follows.

s(t−1)=v0(t−1)+4(t−1)2+C=v0t−v0+4t2+4−8t+C

Hence, distance travelled in the second before a given time is obtained as follows.

s(t)−s(t−1)=v0t+4t2+C−(v0t−v0+4t2+4−8t+C)=v0t+4t2+C−v0t+v0−4t2−4+8t−C=v0+8t−4+(v0t−v0t)+(4t2−4t2)+(C−C)=v0+8t−4

The distance travelled in after the second is obtained by replacing t by t+1 as follows.

s(t+1)=v0(t+1)+4(t+1)2+C=v0t+v0+4t2+4+8t+C

Hence, distance travelled in the second after a given time is obtained as follows.

s(t+1)−s(t)=(v0t+v0+4t2+4+8t+C)−(v0t+4t2+C)=v0t+v0+4t2+4+8t+C−v0t−4t2−C=v0+8t+4+(v0t−v0t)+(4t2−4t2)+(C−C)=v0+8t+4

Calculate difference of the above distances.

s(t+1)−s(t)−s(t−1)+s(t)=v0+8t+4−v0−8t+4s(t+1)−s(t−1)=8

Thus, the given statement is True_.

Answer 12

Ch. 26.1 - In Example 4, change the acceleration to a = 4...Ch. 26.1 - Prob. 2PE Ch. 26.1 - In Example 3, change 5.0 s to 2.5 s and then solve...Ch. 26.1 - Prob. 2E Ch. 26.1 - What is the velocity (in ft/s) of a sandbag 1.5 s...Ch. 26.1 - Prob. 4E Ch. 26.1 - A conveyor belt 8.00 m long moves at 0.25 m/s. If...Ch. 26.1 - Prob. 6E Ch. 26.1 - The velocity (in km/h) of a plane flying into an...Ch. 26.1 - A cyclist goes downhill for 15 min with a velocity...

To decide: Whether the given statement is true or false.

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To decide: Whether the given statement is true or false.

Answer to Problem 1RE

Explanation of Solution

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Chapter 26 Solutions