Understanding Scalar and Vector Quantities - High School Physics
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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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Leslie walks 
north, 
east, 
north, and then 
west before stopping. What is her displacement from her original location?
Leslie walks
Displacement is a vector quantity; it will have both magnitude and direction.
First we need to find his total distance travelled along the y-axis. Let's say that all of her movement north is positive and south is negative.
. She moved a net of 30 meters to the north.
Now let's do the same for the x-axis, using positive for east and negative for west.
. She moved a net of 29 meters to the east.
Now, to find the resultant displacement, we use the Pythagorean Theorem. Her net movement north will be perpendicular to her net movement east, forming a right triangle. Her location relative to her starting point will be the hypotenuse of the triangle.
Now take the square root of both sides.
Since we are solving for a vector, we also need to find the direction of this distance. We do this by solving for the angle of displacement.
To find the angle, we use the arctan of our directional displacements in the x- and y-axes. The tangent of the angle will be equal to the x-displacement over the y-displacement.
Combining the magnitude and direction of our distance gives us the displacement: 
.
Displacement is a vector quantity; it will have both magnitude and direction.
First we need to find his total distance travelled along the y-axis. Let's say that all of her 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. Her net movement north will be perpendicular to her net movement east, forming a right triangle. Her location relative to her starting point will be the hypotenuse of the triangle.
Now take the square root of both sides.
Since we are solving for a vector, we also need to find the direction of this distance. We do this by solving for the angle of displacement.
To find the angle, we use the arctan of our directional displacements in the x- and y-axes. The tangent of the angle will be equal to the x-displacement over the y-displacement.
Combining the magnitude and direction of our distance gives us the displacement:
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Angie runs around a circular track for 
. The track is 
and she runs at a rate of 
. What is her total displacement?
Angie runs around a circular track for
Since she is running on a circular track, every time she makes a loop she has a total displacement of 
. Remember, displacement take into account how far you've travelled, it only uses the total change in distance from where you start and where you stop. Using dimensional analysis, we can determine how many laps she runs in 20 minutes.
After twenty minutes, she has made EXACTLY two loops around the track. That means she is starting and stopping in EXACTLY the same place. Her displacement would be 
, since there is no change between her starting position and her ending position.
Since she is running on a circular track, every time she makes a loop she has a total displacement of
After twenty minutes, she has made EXACTLY two loops around the track. That means she is starting and stopping in EXACTLY the same place. Her displacement would be
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Walter is washing windows on a large building. He starts by washing the window on the 4th floor. He then moves down to the 3rd floor, then up to the 6th floor, then down to the 5th floor, then down to the 2nd floor, and finally he washes the 1st floor window. What is his total displacement?
Walter is washing windows on a large building. He starts by washing the window on the 4th floor. He then moves down to the 3rd floor, then up to the 6th floor, then down to the 5th floor, then down to the 2nd floor, and finally he washes the 1st floor window. What is his total displacement?
Displacement is a vector relating the starting position to the ending position. Displacement does not take into account the route to arrive at the endpoint, and has both magnitude and direction.
In spite of taking a very complicated route to get there, Walter starts at the 4th floor and ends at the 1st floor.
Sine the result is negative, the displacement is 3 floors downward.
Displacement is a vector relating the starting position to the ending position. Displacement does not take into account the route to arrive at the endpoint, and has both magnitude and direction.
In spite of taking a very complicated route to get there, Walter starts at the 4th floor and ends at the 1st floor.
Sine the result is negative, the displacement is 3 floors downward.
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Walter is washing windows on a large building. He starts by washing the window on the 4th floor, then down to the 3rd floor, then up to the 6th floor, then down to the 5th floor, then down to the 2nd floor, and finally he washes the 1st floor window. What is his total distance?
Walter is washing windows on a large building. He starts by washing the window on the 4th floor, then down to the 3rd floor, then up to the 6th floor, then down to the 5th floor, then down to the 2nd floor, and finally he washes the 1st floor window. What is his total distance?
Distance is a scalar quantity and will take into account only the number of floors travelled, regardless of the direction of movement.
Walter takes an incredibly complicated path to wash the windows on the building. When calculating distance, we add up all the movement he does, regardless of direction.
First, he travels down one floor (4th to 3rd).
Then he travels up three floors (3rd to 6th).
Then he travels down one floor (6th to 5th), then down another three floors (5th to 2nd).
Finally, he travels down one more floor (2nd to 1st).
In total, Walter travelled 
.
Distance is a scalar quantity and will take into account only the number of floors travelled, regardless of the direction of movement.
Walter takes an incredibly complicated path to wash the windows on the building. When calculating distance, we add up all the movement he does, regardless of direction.
First, he travels down one floor (4th to 3rd).
Then he travels up three floors (3rd to 6th).
Then he travels down one floor (6th to 5th), then down another three floors (5th to 2nd).
Finally, he travels down one more floor (2nd to 1st).
In total, Walter travelled
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Ariel walks 
to the east, 
to the west, and then 
to the east again. What is her total displacement?
Ariel walks
Displacement is a vector quantity, with both magnitude and direction. Remember, displacement does not take into account the route traveled, only the difference between starting position and ending position.
All movement in this question occurs along the x-axis (east and west. We use positive for east and negative for west, since direction is important to measure displacement.
This means that her total displacement was 
.
Displacement is a vector quantity, with both magnitude and direction. Remember, displacement does not take into account the route traveled, only the difference between starting position and ending position.
All movement in this question occurs along the x-axis (east and west. We use positive for east and negative for west, since direction is important to measure displacement.
This means that her total displacement was
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Which of these is a vector quantity?
Which of these is a vector quantity?
Scalar quantities give a magnitude, while vector quantities give a magnitude and a direction. The answer will be a measurement that must act in a given direction.
Distance is a measure of length, regardless of the direction. Displacement is the vector equivalent of distance.
Speed is a measure of rate, regardless of direction. Velocity is the vector equivalent of speed.
Temperature and time do not act in any direction and are purely scalar.
Acceleration must act in a given direction, and is a vector. An acceleration is described by both a magnitude and a direction of action.
Scalar quantities give a magnitude, while vector quantities give a magnitude and a direction. The answer will be a measurement that must act in a given direction.
Distance is a measure of length, regardless of the direction. Displacement is the vector equivalent of distance.
Speed is a measure of rate, regardless of direction. Velocity is the vector equivalent of speed.
Temperature and time do not act in any direction and are purely scalar.
Acceleration must act in a given direction, and is a vector. An acceleration is described by both a magnitude and a direction of action.
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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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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 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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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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Two vectors each have a magnitude of 
. Consider the range of possible lengths of the vector sum (resultant vector) of the two vectors, depending on their directions. What is the difference in magnitude between the largest possible length and the smallest possible length of the resultant vector?
Two vectors each have a magnitude of
The largest possible length of the vector sum of the two vectors results when the vectors are oriented in the same direction. In this scenario, the resultant vector will have a length equal to the sum of the magnitudes of the two vectors.
The smallest possible length of the vector sum results when the vectors are oriented in opposite directions. In this scenario, the resultant vector will have a length equal to the different in magnitude between the two vectors.
The largest magnitude of the resultant vector is 
and the smallest is 
. Now we need to find the difference between these magnitudes.
The largest possible length of the vector sum of the two vectors results when the vectors are oriented in the same direction. In this scenario, the resultant vector will have a length equal to the sum of the magnitudes of the two vectors.
The smallest possible length of the vector sum results when the vectors are oriented in opposite directions. In this scenario, the resultant vector will have a length equal to the different in magnitude between the two vectors.
The largest magnitude of the resultant vector is
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Which of these is not a vector quantity?
Which of these is not a vector quantity?
A scalar quantity can be defined by magnitude alone, but a vector quantity has both magnitude and direction of action. Mass is a scalar quantity because it does not act in any particular direction. The phrase "five kilograms east" is nonsense, indicating the mass cannot be a vector.
Angular momentum, force, displacement, and torque are all vector quantities and describe a value applied in a certain direction.
A scalar quantity can be defined by magnitude alone, but a vector quantity has both magnitude and direction of action. Mass is a scalar quantity because it does not act in any particular direction. The phrase "five kilograms east" is nonsense, indicating the mass cannot be a vector.
Angular momentum, force, displacement, and torque are all vector quantities and describe a value applied in a certain direction.
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Express a vector with magnitude 2.24 directed 63.4° CCW from the x-axis in unit vector form.
Express a vector with magnitude 2.24 directed 63.4° CCW from the x-axis in unit vector form.
The x-coordinate is the magnitude times the cosine of the angle, while the y-coordinate is the magnitude times the sine of the angle.
The resultant vector is: 
.
The x-coordinate is the magnitude times the cosine of the angle, while the y-coordinate is the magnitude times the sine of the angle.
The resultant vector is:
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What is the magnitude and angle for the following vector, measured CCW from the x-axis?
What is the magnitude and angle for the following vector, measured CCW from the x-axis?
The magnitude of the vector is found using the distance formula:
To calculate the angle we must first find the inverse tangent of 
:
This angle value is the principal arctan, but it is in the fourth quadrant while our vector is in the second. We must add the angle 180° to this value to arrive at our final answer.
The magnitude of the vector is found using the distance formula:
To calculate the angle we must first find the inverse tangent of
This angle value is the principal arctan, but it is in the fourth quadrant while our vector is in the second. We must add the angle 180° to this value to arrive at our final answer.
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