High college Physics assist » Introductory values » expertise Scalar and also Vector quantities
Explanation:

The difference between a scalar and a vector is the a vector calls for a direction. Scalar quantities have only magnitude; vector quantities have both magnitude and direction. Time is completely separated native direction; that is a scalar. It has only magnitude, no direction.

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Force, displacement, and acceleration all occur with a designated direction.

Important distinctions to know:

Speed is a scalar, when velocity is a vector.

Distance is a scalar, if displacement is a vector.

Force and acceleration room vectors. Time is a scalar.


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Example inquiry #2 : understanding Scalar and also Vector quantities


Which the the adhering to is a vector quantity?


Possible Answers:

Displacement


Speed


Distance


All that these room vector quantities


Time


Correct answer:

Displacement


Explanation:

A vector has both magnitude and also direction, when a scalar has only magnitude. Ask yourself, "for i m sorry of these points is there a direction?" for displacement, we would certainly say "50 meters NORTH," whereas v the others, we would certainly say "50 meters," "20 seconds," or "30 miles per hour."

Important distinctions come know:

Speed is a scalar, when velocity is a vector.

Distance is a scalar, when displacement is a vector.

Force and also acceleration space vectors. Time is a scalar.


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Example concern #3 : understanding Scalar and Vector quantities


Michael walks 

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 north, 
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 west, 
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 south, 
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 east, and also then stop to catch his breath. What is the magnitude of his displacement indigenous his original point?


Possible Answers:

*


*


*



*


Correct answer:


Explanation:

Displacement is a vector quantity; the direction the Michael travels will be either optimistic or an adverse along one axis. We are being request to solve for his position relative come his beginning point, not for the street he has actually walked.

First we require to find his total distance travelled along the y-axis. Let"s to speak that all of his activity north is positive and south is negative.

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. He moved a net of 5 meter to the north along the y-axis.

Now let"s carry out the same for the x-axis, using positive for eastern and negative for west.

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. He moved a network of 9 meters to the east.

Now to discover the resultant displacement, we usage the Pythagorean Theorem. The net motion north will be perpendicular to the net motion east, creating a appropriate triangle. Michael"s place relative come his starting point will certainly be the hypotenuse of this triangle.

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*

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Now take it the square root of both sides.

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*

Since the difficulty only asks for the magnitude of the displacement, we perform not require to carry out the direction.


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Example inquiry #4 : expertise Scalar and Vector quantities


Leslie go

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 north, 
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 east, 
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 north, and also then 
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 west prior to stopping. What is her displacement from her original location?


Possible Answers:
Correct answer:

*


Explanation:

Displacement is a vector quantity; that will have both magnitude and also direction.

First we require to uncover his total distance took trip along the y-axis. Let"s say that all of her movement north is positive and also south is negative.

*
. She moved a network of 30 meters to the north. 

Now let"s perform the exact same for the x-axis, using optimistic for east and an adverse for west.

*
. She moved a network of 29 meters to the east.

Now, to find the resultant displacement, we usage the Pythagorean Theorem. Her net movement north will be perpendicular to she net activity east, creating a ideal triangle. Her location relative come her beginning point will certainly be the hypotenuse of the triangle.

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*

*

*

Now take the square source of both sides.

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*

Since we are addressing for a vector, we also need to find the direction the this distance. We execute this by addressing for the angle of displacement.

To uncover the angle, we use the arctan of our directional displacements in the x- and also y-axes. The tangent that the angle will certainly be same to the x-displacement end the y-displacement.

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*

*

*

*

Combining the magnitude and direction of our distance offers us the displacement:

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.