Scalars & VectorsScalars & VectorsScalars & VectorsScalars & Vectors

Scalars:• Measurements that have no direction• The quantity is called magnitude • Ex: Distance: d, time: t, mass: mVectors:• Measurements that have both direction & magnitude• Indicate direction with +/- sign or [N], [E], [W], [S]• Must put arrow over vector symbols• Ex: Displacement: ,velocity: ,force:

Scalars vs. VectorsScalars vs. VectorsScalars vs. VectorsScalars vs. Vectors

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During calculations, vectors that are:• Up and right are positive (+ve)• Down & left are negative (-ve)

**But usually you specify thedirection of vectors in the final “answer” (N, E, W, S)

Vector Sign ConventionsVector Sign ConventionsVector Sign ConventionsVector Sign Conventions

+ve

+ve-ve

-ve

[N]

[E][W]

[S]

Distance (d): • Length travelled by an object regardless of direction. • Scalar = Always +veDisplacement ( ): • Change in position of an object.

= final position – initial position• Vector– If ∆d = +ve, object moves right or up– If ∆d = -ve, object moves left or down

***Displacement is independent of path taken.

Distance vs. DisplacementDistance vs. DisplacementDistance vs. DisplacementDistance vs. Displacement

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Ex: A student walks 5 m east and then 3 m west.a)What is the distance travelled?b)What is the student’s displacement?

a) d = 5 m + 3 m = 8 mb) Draw the vector arrows:

5 m east

3 m west

Resultant or “net” vector

2 m east

When adding vectors we use theWhen adding vectors we use the tip-to-tail method.tip-to-tail method.

You try:A man walks 275 m east and then turns around

and walks 425 m west. He then returns to where he started.

a)What was the distance travelled by the man?b)What was the man’s displacement?