002Velocity

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course Phy 241

002. Velocity*********************************************

Question: `q001. Note that there are 17 questions in this assignment.

If an object moves 12 meters in 4 seconds, then what is its average velocity? Explain how you obtained your result in terms of commonsense ideas.

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Your solution: 12 meters / 4 seconds is 3meters per second. Velocity is the rate of change, in this case, of distance with respect to time. You

are trying to determine the average distance moved in the specified time (seconds).

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Question: `q002. How is the preceding problem related to the concept of a rate?

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Your solution: A rate is a specific ratio of two measurements. Velocity is a rate.

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Question: `q003. We are still referring to the situation of the preceding questions:

Is object position dependent on time or is time dependent on object position?

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Your solution: Object position is dependent on time. Time will continue whether the object is moving or not, making it independent of the

position of the object.

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Question: `q004. We are still referring to the situation of the preceding questions, which concern average velocity:

So the rate here is the average rate at which position is changing with respect to clock time. Explain what concepts, if any, you missed in your

explanations.

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Your solution: We do not take into consideration direction or path that object traveled, we assume it is in a straight line in our calculations.

We also assume it is at constant speed, no incline or anything like that.

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Question: `q005. If an object is displaced -6 meters in three seconds, then what is the average speed of the object? What is its average

velocity? Explain how you obtained your result in terms of commonsense images and ideas.

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Your solution: The average speed is 6 meters / 3 seconds = 2 meters per second. Velocity is the same but direction is involved with velocity. It

would be negative 6 meters per second, possible backwards or downwards movement. Speed tells you how fast or slow an object is moving, velocity

tells you in which direction the distance is being took.

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Question: `q006. If `ds stands for the change in the position of an object and `dt for the time interval during which its position changes,

then what expression stands for the average velocity vAve of the object during this time interval?

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Your solution: vAve = `ds /`dt ; Average velocity = change in position of the object divided by the time interval suring which the position

changed.

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Question: `q007. How do you write the expressions `ds and `dt on your paper?

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Your solution: `d is the typewriter shortcut for the greek symbol Delta. Delta means change and is written like a tiny triangle.

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Question: `q008. If an object changes position at an average rate of 5 meters/second for 10 seconds, then how far does it move?

How is this problem related to the concept of a rate?

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Your solution: 10 seconds * (5 meters / second) = 50 meters. The object traveled 50 meters in 10 seconds at the rate of 5 meters per second.

This problem uses a rate to find one of the quantities instead of using the quantities to find a rate.

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Question: `q009. If vAve stands for the rate at which the position of the object changes with respect to clock time (also called velocity) and

`dt for the time interval during which the change in position is to be calculated, then how to we write the expression for the change `ds in the

position?

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Your solution: `ds = vAve * `dt

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Question: `q010. Explain how the quantities average velocity vAve, time interval `dt and displacement `ds are related by the definition of a

rate, and how this relationship can be used to solve the current problem.

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Your solution: All three quantities are related. Just as vAve = `ds / `dt, 'ds = vAve * 'dt and `dt = `ds / vAve. we can use and of these three

properties of the equation to find the missing piece.

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Question: `q011. The basic rate relationship vAve = `ds / `dt expresses the definition of average velocity vAve as the rate at which position s

changes with respect to clock time t. What algebraic steps do we use to solve this equation for `ds, and what is our result?

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Your solution: vAve = `ds / `dt: First, multiply each side of the equation by `dt. `dt cancels out on the right hand side and leave vAve * `dt =

`ds.

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Question: `q012. How is the preceding result related to our intuition about the meanings of the terms average velocity, displacement and clock

time?

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Your solution: The equation reads as the displacement is equal to the average velocity multiplied by clock time .

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Question: `q013. What algebraic steps do we use to solve the equation vAve = `ds / `dt for `dt, and what is our result?

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Your solution: vAve = `ds / `dt: First multiply both sides by `dt. [ (`dt) vAve = `ds / `dt (`dt)] On the right side `dt will divide out leaving

`dt * vAve = `ds. Then you would divide each side, again, by vAve: [ ( vAve) `dt * vAve = `ds ( vAve) ] On the left side the vAve will divide

leaving `dt = `ds * vAve, our new equation.

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Question: `q014. How is this result related to our intuition about the meanings of the terms average velocity, displacement and clock time?

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Your solution: The equation reads as the clock time is equal to the average velocity multiplied by the displacement.

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Question: `q015. A ball falls 20 meters from rest in 2 seconds. What is the average velocity of its fall?

Your answer should begin with the definition of average velocity, in terms of the definition of an average rate of change.

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Your solution: Average velocity is the rate of change in position with respect to clock time in this equation. The ball falls at a rate of 10

meters per second; 20 meters / 2 seconds = 10 meters per second.

Confidence: OK

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Question: `q016. A car moves at an average speed of 20 m/s for 6 seconds. How far does it move?

Your answer should begin with the definition of average velocity, in terms of the definition of an average rate of change.

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Your solution: In this problem we are solving for `ds. 20 m/s * 6 seconds = `ds = 120 meters. The car moved 120 meters in 6 seconds.

Confidence: OK

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Question: `q017. An object's position changes by amount `ds during a time interval `dt. What is the expression for its average velocity during

this interval?

Your answer should begin with the definition of average velocity, in terms of the definition of an average rate of change.

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Your solution: Average velocity, as stated in this problem, is the objects change in position divided by the tim einterval during which it

changes position: vAve = `ds / `dt

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