Introductory Principles - Physics
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Which of the following is a vector quantity?
Which of the following is a vector quantity?
A vector quantity is described by both its magnitude, and its direction of action. In contrast, a scalar quantity is described only by its magnitude.
Force is a vector because the direction of action is relevant to describing the force. An upward force is notably different from a downward force.
Voltage, resistance, charge, and electric potential are scalar quantities and are the same regardless of any direction of action. For example, turning a circuit sideways does not alter the values for any of these quantities.
A vector quantity is described by both its magnitude, and its direction of action. In contrast, a scalar quantity is described only by its magnitude.
Force is a vector because the direction of action is relevant to describing the force. An upward force is notably different from a downward force.
Voltage, resistance, charge, and electric potential are scalar quantities and are the same regardless of any direction of action. For example, turning a circuit sideways does not alter the values for any of these quantities.
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Which of these is used to describe both scalar and vector quantities?
Which of these is used to describe both scalar and vector quantities?
Vector quantities are defined by both a direction and a magnitude. Force, velocity, acceleration, and momentum are all vectors.
Scalar quantities are defined only by a magnitude. Mass, time, speed, and voltage are all scalars.
Vector and scalar quantities both require a magnitude.
Vector quantities are defined by both a direction and a magnitude. Force, velocity, acceleration, and momentum are all vectors.
Scalar quantities are defined only by a magnitude. Mass, time, speed, and voltage are all scalars.
Vector and scalar quantities both require a magnitude.
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Which of these is a scalar quantity?
Which of these is a scalar quantity?
Scalar quantities give a magnitude, while vector quantities give a magnitude and a direction. The answer will be a measurement that does not change, regardless of the direction of action.
Displacement is a measure of length in a given direction; distance is the scalar version of displacement.
Velocity is a measure of rate in a given direction; speed is the scalar version of velocity.
Force is a derivative of acceleration, and can only act in a given direction. There is no scalar equivalent of force. Similarly, momentum is a derivative of velocity and has no scalar equivalent.
Mass is a measure solely of magnitude, and requires no direction of action. Mass is a scalar quantity.
Scalar quantities give a magnitude, while vector quantities give a magnitude and a direction. The answer will be a measurement that does not change, regardless of the direction of action.
Displacement is a measure of length in a given direction; distance is the scalar version of displacement.
Velocity is a measure of rate in a given direction; speed is the scalar version of velocity.
Force is a derivative of acceleration, and can only act in a given direction. There is no scalar equivalent of force. Similarly, momentum is a derivative of velocity and has no scalar equivalent.
Mass is a measure solely of magnitude, and requires no direction of action. Mass is a scalar quantity.
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A dog starts next to his owner, runs 
to chase a ball, and then runs back 
to the person who threw it. If this happens eight times to completion, what is the dog's displacement?
A dog starts next to his owner, runs
Displacement is a vector quantity that describes final positive relative to the starting point. It only measures the change in distance from where you start to where you end up.
Since the dog runs away, and then runs back to his original starting point, he is going a total displacement of zero meters for every loop. Since he makes eight full circuits, he will start and end in exactly the same place, hence, 
displacement.
Distance is the scalar equivalent for displacement; the dog's distance traveled with be 
.
Displacement is a vector quantity that describes final positive relative to the starting point. It only measures the change in distance from where you start to where you end up.
Since the dog runs away, and then runs back to his original starting point, he is going a total displacement of zero meters for every loop. Since he makes eight full circuits, he will start and end in exactly the same place, hence,
Distance is the scalar equivalent for displacement; the dog's distance traveled with be
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A dog runs 
to chase a ball and then runs back 
to the person who threw it. If this happens eight times to completion, what is the dog's distance travelled?
A dog runs
Unlike displacement, which only measures the change between starting point and ending point, distance measures the entire trip travelled. Displacement is a vector, while distance is a scalar; thus, displacement is independent of path, while distance is dependent on path.
Each circuit the dog travels a total of 
, and he makes this trip eight times.
He will travel a total distance of 
.
The total displacement would be zero because the dog's ending position does not change, relative to his starting position.
Unlike displacement, which only measures the change between starting point and ending point, distance measures the entire trip travelled. Displacement is a vector, while distance is a scalar; thus, displacement is independent of path, while distance is dependent on path.
Each circuit the dog travels a total of
He will travel a total distance of
The total displacement would be zero because the dog's ending position does not change, relative to his starting position.
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Michael's scale measures the mass of objects as consistently 
less than their actual mass. How would you describe the scale?
Michael's scale measures the mass of objects as consistently
Precision measures is how consistently a device records the same answer. In this case, Michael's scale is ALWAYS 
short. Even though it displays the wrong value, it is consistent. That means it is precise. Measuring a 
object will always display a mass of 
; the results are easily reproduced.
Accuracy is how well a device measures something against its accepted value. In this case, Michael's scale is not accurate because it is always off by 
.
Precision measures is how consistently a device records the same answer. In this case, Michael's scale is ALWAYS
Accuracy is how well a device measures something against its accepted value. In this case, Michael's scale is not accurate because it is always off by
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Michael buys several bags of balloons. On the package, it says that each bag has 100 balloons. He opens the bags and only one of them has 100 balloons inside; the other bags either have too many or too few.
How would you describe the bag of balloons with 100 balloons inside?
Michael buys several bags of balloons. On the package, it says that each bag has 100 balloons. He opens the bags and only one of them has 100 balloons inside; the other bags either have too many or too few.
How would you describe the bag of balloons with 100 balloons inside?
This bag is accurate because it provided the correct number of balloons, however, the process is not precise as the results were clearly not repeatable.
Accuracy deals with how close the measurement got to the accepted measurement. Precision deals with how consistent the measurement is. The bag with 100 balloons inside matched the claim made on the bag, meaning it was accurate. It was not precise because the other measurements show that the number of balloons is variable.
This bag is accurate because it provided the correct number of balloons, however, the process is not precise as the results were clearly not repeatable.
Accuracy deals with how close the measurement got to the accepted measurement. Precision deals with how consistent the measurement is. The bag with 100 balloons inside matched the claim made on the bag, meaning it was accurate. It was not precise because the other measurements show that the number of balloons is variable.
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An brand of fruit snacks claims that each bag of fruit snacks has a mass of 
. After weighing three bags, Wally observes the masses to be 
, 
, and 
.
How can Wally describe the accuracy and precision of the first bag he measured?
An brand of fruit snacks claims that each bag of fruit snacks has a mass of
How can Wally describe the accuracy and precision of the first bag he measured?
The claim for the mass of the first bag is accurate; the brand says there should be 
in each bag and there was 
in the first bag.
The claim on the first bag is not precise, as the results are not replicated universally throughout the experiment. The masses of the bags fluctuate, with the average of all three bags equal to 
.
The claim for the mass of the first bag is accurate; the brand says there should be
The claim on the first bag is not precise, as the results are not replicated universally throughout the experiment. The masses of the bags fluctuate, with the average of all three bags equal to
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A bowman is shooting arrows at a target. Which of the following demonstrates high accuracy but low precision?
A bowman is shooting arrows at a target. Which of the following demonstrates high accuracy but low precision?
Accuracy is measured as the degree of closeness to the actual measurement. In our case, accurate shots will hit the bullseye. Precision is measured as the degree of closeness of one measurement to the next. In our case, precise shots will be clustered together.
To get high accuracy but low precision, measurements must center around the target value but be variable. The bowman's arrows will not be clustered (low precision), but will be accurately distributed around the bullseye. If all the shots were averaged, the bullseye would be at the center.
Accuracy is measured as the degree of closeness to the actual measurement. In our case, accurate shots will hit the bullseye. Precision is measured as the degree of closeness of one measurement to the next. In our case, precise shots will be clustered together.
To get high accuracy but low precision, measurements must center around the target value but be variable. The bowman's arrows will not be clustered (low precision), but will be accurately distributed around the bullseye. If all the shots were averaged, the bullseye would be at the center.
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Which of the following is not a vector quantity?
Which of the following is not a vector quantity?
Vector quantities have both magnitude and direction, while scalar quantities have only magnitude.
Velocity, acceleration, force, and displacement are all vectors. They must have a magnitude, as well as a direction of action. A velocity can be 
to the north, and a displacement can be 
east. A good way to identify vectors is if they can be negative. A negative vector indicates "downward" or "to the left," while a negative scalar cannot exist.
Volume is not a vector; it cannot have a direction. An object cannot have a volume of 
to the left, not can it have a volume of 
.
Vector quantities have both magnitude and direction, while scalar quantities have only magnitude.
Velocity, acceleration, force, and displacement are all vectors. They must have a magnitude, as well as a direction of action. A velocity can be
Volume is not a vector; it cannot have a direction. An object cannot have a volume of
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Which of these is an example of high accuracy?
Which of these is an example of high accuracy?
Accuracy is the measure of difference between a calculated value and the true value of a measurement. High accuracy demands that the experimental result be equal to the theoretical result.
In contrast, precision is a measure of reproducibility. If multiple trials produce the same result each time with minimal deviation, then the experiment has high precision. This is true even if the results are not true to the theoretical predictions; an experiment can have high precision with low accuracy.
An archer hitting a bulls-eye is an example of high accuracy, while an archer hitting the same spot on the bulls-eye three times would be an example of high precision.
Accuracy is the measure of difference between a calculated value and the true value of a measurement. High accuracy demands that the experimental result be equal to the theoretical result.
In contrast, precision is a measure of reproducibility. If multiple trials produce the same result each time with minimal deviation, then the experiment has high precision. This is true even if the results are not true to the theoretical predictions; an experiment can have high precision with low accuracy.
An archer hitting a bulls-eye is an example of high accuracy, while an archer hitting the same spot on the bulls-eye three times would be an example of high precision.
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Which of these is an example of high precision?
Which of these is an example of high precision?
Precision is a measure of reproducibility. If multiple trials produce the same result each time with minimal deviation, then the experiment has high precision. This is true even if the results are not true to the theoretical predictions; an experiment can have high precision with low accuracy.
In contrast, accuracy is the measure of difference between a calculated value and the true value of a measurement. High accuracy demands that the experimental result be equal to the theoretical result.
An archer hitting a bulls-eye is an example of high accuracy, while an archer hitting the same spot on the bulls-eye three times would be an example of high precision.
Precision is a measure of reproducibility. If multiple trials produce the same result each time with minimal deviation, then the experiment has high precision. This is true even if the results are not true to the theoretical predictions; an experiment can have high precision with low accuracy.
In contrast, accuracy is the measure of difference between a calculated value and the true value of a measurement. High accuracy demands that the experimental result be equal to the theoretical result.
An archer hitting a bulls-eye is an example of high accuracy, while an archer hitting the same spot on the bulls-eye three times would be an example of high precision.
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A scientist measures how far a particle travels within a given amount of time. Every second she measures how far it has gone, and creates a graph of her results. What is the independent variable in this experiment?
A scientist measures how far a particle travels within a given amount of time. Every second she measures how far it has gone, and creates a graph of her results. What is the independent variable in this experiment?
An independent variable is manipulated by the experimenter. Any changes made are predictable. The dependent variable reacts to changes made to the independent variable. Its changes are not controlled by the experimenter and can be hard to predict.
In this particular experiment, the scientist is measuring how the particle's distance changes over a given time. She is able to control the amount of time that she measures, but is only able to observe the distance traveled.
In the graph, the independent variable will be graphed on the x-axis.
An independent variable is manipulated by the experimenter. Any changes made are predictable. The dependent variable reacts to changes made to the independent variable. Its changes are not controlled by the experimenter and can be hard to predict.
In this particular experiment, the scientist is measuring how the particle's distance changes over a given time. She is able to control the amount of time that she measures, but is only able to observe the distance traveled.
In the graph, the independent variable will be graphed on the x-axis.
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When looking at velocity in terms of distance and time, what is the independent variable?
When looking at velocity in terms of distance and time, what is the independent variable?
There are a few ways to think of this question. The first is to imagine you are graphing velocity. Since the equation is 
, the displacement would be on the y-axis and time would be on the x-axis. The x-axis is going to be where we put our independent variable.
The other way to think of this is to ask yourself what our "inputs" and "outputs" would be if we were measuring velocity. Imagine you're walking down the street and you record how far you travel every second. The time is what you are "inputting" and your distance travelled is your "output."
There are a few ways to think of this question. The first is to imagine you are graphing velocity. Since the equation is
The other way to think of this is to ask yourself what our "inputs" and "outputs" would be if we were measuring velocity. Imagine you're walking down the street and you record how far you travel every second. The time is what you are "inputting" and your distance travelled is your "output."
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You are looking at a graph of the motion of a vehicle. On the y-axis is displacement and on the x-axis is time. Which of the following is the independent variable?
You are looking at a graph of the motion of a vehicle. On the y-axis is displacement and on the x-axis is time. Which of the following is the independent variable?
Independent variables are predetermined by the experimenter and can be manipulated to change the measured dependent variable. Independent variables are generally graphed on the x-axis, while dependent variables are generally graphed on the y-axis.
In this question, time is the independent variable and displacement is the dependent variable. The experimenter can select sampling times, but cannot necessarily predict the displacement that will be measured at each point. This defines time as the independent variable.
Independent variables are predetermined by the experimenter and can be manipulated to change the measured dependent variable. Independent variables are generally graphed on the x-axis, while dependent variables are generally graphed on the y-axis.
In this question, time is the independent variable and displacement is the dependent variable. The experimenter can select sampling times, but cannot necessarily predict the displacement that will be measured at each point. This defines time as the independent variable.
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Which of the following is a vector?
Which of the following is a vector?
Remember, vectors need both magnitude and direction. Acceleration is the only answer choice that requires both magnitude and direction.
Remember, vectors need both magnitude and direction. Acceleration is the only answer choice that requires both magnitude and direction.
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Where is the independent variable most commonly displayed on a graph?
Where is the independent variable most commonly displayed on a graph?
The independent variable is controlled by the experimenter, while the dependent variable will fluctuate based on independent variable inputs. The independent variable is always displayed on the x-axis of a graph, while the dependent variable appears on the y-axis. Time is a common independent variable, as it will not be affeced by any dependent environemental inputs. Time can be treated as a controllable constant against which changes in a system can be measured.
The independent variable is controlled by the experimenter, while the dependent variable will fluctuate based on independent variable inputs. The independent variable is always displayed on the x-axis of a graph, while the dependent variable appears on the y-axis. Time is a common independent variable, as it will not be affeced by any dependent environemental inputs. Time can be treated as a controllable constant against which changes in a system can be measured.
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Which of the following is a vector quantity?
Which of the following is a vector quantity?
A vector has both magnitude and direction, while a scalar has only magnitude. Ask yourself, "for which of these things is there a direction?" For displacement, we would say "50 meters NORTH," whereas with the others, we would say "50 meters," "20 seconds," or "30 miles per hour."
Important distinctions to know:
Speed is a scalar, while velocity is a vector.
Distance is a scalar, while displacement is a vector.
Force and acceleration are vectors. Time is a scalar.
A vector has both magnitude and direction, while a scalar has only magnitude. Ask yourself, "for which of these things is there a direction?" For displacement, we would say "50 meters NORTH," whereas with the others, we would say "50 meters," "20 seconds," or "30 miles per hour."
Important distinctions to know:
Speed is a scalar, while velocity is a vector.
Distance is a scalar, while displacement is a vector.
Force and acceleration are vectors. Time is a scalar.
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Which of the following is a scalar quantity?
Which of the following is a scalar quantity?
The difference between a scalar and a vector is that a vector requires a direction. Scalar quantities have only magnitude; vector quantities have both magnitude and direction. Time is completely separated from direction; it is a scalar. It has only magnitude, no direction.
Force, displacement, and acceleration all occur with a designated direction.
Important distinctions to know:
Speed is a scalar, while velocity is a vector.
Distance is a scalar, while displacement is a vector.
Force and acceleration are vectors. Time is a scalar.
The difference between a scalar and a vector is that a vector requires a direction. Scalar quantities have only magnitude; vector quantities have both magnitude and direction. Time is completely separated from direction; it is a scalar. It has only magnitude, no direction.
Force, displacement, and acceleration all occur with a designated direction.
Important distinctions to know:
Speed is a scalar, while velocity is a vector.
Distance is a scalar, while displacement is a vector.
Force and acceleration are vectors. Time is a scalar.
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Michael walks 
north, 
west, 
south, 
east, and then stops to catch his breath. What is the magnitude of his displacement from his original point?
Michael walks
Displacement is a vector quantity; the direction that Michael travels will be either positive or negative along an axis. We are being asked to solve for his position relative to his starting point, NOT for the distance he has walked.
First we need to find his total distance travelled along the y-axis. Let's say that all of his movement north is positive and south is negative.
. He moved a net of 5 meters to the north along the y-axis.
Now let's do the same for the x-axis, using positive for east and negative for west.
. He moved a net of 9 meters to the east.
Now to find the resultant displacement, we use the Pythagorean Theorem. The net movement north will be perpendicular to the net movement east, forming a right triangle. Michael's position relative to his starting point will be the hypotenuse of this triangle.
Now take the square root of both sides.
Since the problem only asks for the magnitude of the displacement, we do not need to provide the direction.
Displacement is a vector quantity; the direction that Michael travels will be either positive or negative along an axis. We are being asked to solve for his position relative to his starting point, NOT for the distance he has walked.
First we need to find his total distance travelled along the y-axis. Let's say that all of his movement north is positive and south is negative.
Now let's do the same for the x-axis, using positive for east and negative for west.
Now to find the resultant displacement, we use the Pythagorean Theorem. The net movement north will be perpendicular to the net movement east, forming a right triangle. Michael's position relative to his starting point will be the hypotenuse of this triangle.
Now take the square root of both sides.
Since the problem only asks for the magnitude of the displacement, we do not need to provide the direction.
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