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?