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Definitions
Scalar: A physical quantity with magnitude only.
Vector: A physical quantity with both magnitude and direction.

Watch this video.

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Compared and contrasted, plus examples

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VECTOR DIRECTIONS EXPRESSED IN TWO WAYS:

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VECTOR DIRECTIONS EXPRESSED IN TWO WAYS:

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1. Cardinal directions (NEWS)

2. Bearing (clockwise from North)

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INTRODUCTION TO MECHANICS & WORKING OUT DISTANCE VS DISPLACEMENT

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INTRODUCTION TO MECHANICS & WORKING OUT DISTANCE VS DISPLACEMENT

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As part of our study of Vectors, we need to introduce the following concepts: distance, displacement, speed, velocity and acceleration.

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DISTANCE (d)

Distance:  The magnitude of the actual distance covered by a moving object from the starting point to the finishing point.

DISPLACEMENT (Δx)

Displacement (Δx): The magnitude and direction of the straight-line distance from the starting point to the end point of a motion.

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DISTANCE VS DISPLACEMENT - WATCH THIS VIDEO:

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DISTANCE VS DISPLACEMENT - WATCH THIS VIDEO:

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Definition:
Velocity is the rate of displacement.
Or The rate of change in position.

Remember: "rate" means "per unit time".

Velocity is a vector quantity and is measured in m.s⁻¹.

Average velocity is calculated using the following equation:

𝐴𝑣𝑒𝑟𝑎𝑔𝑒 𝑣𝑒𝑙𝑜𝑐𝑖𝑡𝑦 = 𝑑𝑖𝑠𝑝𝑙𝑎𝑐𝑒𝑚𝑒𝑛𝑡/𝑡𝑖𝑚𝑒

𝒗𝒂𝒗 = ∆𝒙 / ∆𝑡

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Examples on Distance vs Displacement and Speed vs Velocity

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WITH ANSWERS

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WITH ANSWERS

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DEF:
RESULTANT = the single vector which has the same effect as the original vectors acting together.

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RESULTANT = the single vector which has the same effect as the original vectors acting together.

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RESULTANT = the single vector which has the same effect as the original vectors acting together.

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Click on the link below to do an interactive simulation activity on how to add vectors.

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Remember:
RESULTANT = the single vector which has the same effect as the original vectors acting together.
Calculate the magnitude of the resultant vector, R, in the examples below (use Pythagoras):

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HOW TO DETERMINE THE VECTOR DIRECTION USING SIMPLE TRIG

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HOW TO DETERMINE THE VECTOR DIRECTION USING SIMPLE TRIG

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RESULTANT = the single vector which has the same effect as the original vectors acting together.

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A girl walks a distance of 100 m due east before turning and walking a distance of  50 m in a direction E 60o S.  Determine her resultant displacement by accurate construction and measurement.
Remember:
RESULTANT = the single vector which has the same effect as the original vectors acting together.

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VECTORS BY CONSTRUCTION: ANSWERS TO EXAMPLE 2 - PAGE 6 OF THE NOTES

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VECTORS BY CONSTRUCTION: ANSWERS TO EXAMPLE 2 - PAGE 6 OF THE NOTES

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HEAD-TO-TAIL METHOD

TAIL-TO-TAIL METHOD

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1. ADDING VECTORS USING THE TRIANGLE METHOD 

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1. ADDING VECTORS USING THE TRIANGLE METHOD 

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HEAD-TO-TAIL METHOD

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TAIL-TO-TAIL METHOD

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Watch this video (if watching on a cell phone, click the diagonal arrow icon):

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It means:
Breaking up a skew vector into horizontal and vertical dimensions (lengths).
Horizontal component =  R x
Vertical component = R y
Do the example below: