Review: Vector vs. Scalar Quantities
Scalar ­­ reports magnitude only.
Vector ­­ reports magnitude and direction
1
Do Now: Dorothy is walking Toto. Dorothy's path is shown in blue, Toto's path is in dashed black. Who has traveled further?
1
A
Dorothy
B
Toto
C
neither
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Distance vs. Displacement
Distance is a scalar quantity which describes "how much ground" the object has covered during motion.
Displacement is a vector quantity which describes the change in position of the object from starting point to ending point (i.e. vector starting at the starting point and ending at the ending point)
3
Use the diagram below to determine the resulting displacement and distance traveled by the skier in 3 minutes (the skier traveled from A to B to C to D)
The skier covers a distance of (180 m + 140 m + 100 m) = 420 m
and has a displacement of 140 m, to the right.
4
A football coach paces back and forth along the sidelines. The diagram below shows several of coach's positions at various times. At each marked position, the coach makes a "U­turn" and moves in the opposite direction. In other words, he moves from A to B to C to D.
Determine the resulting displacement and distance of travel.
5
Is it possible to have a case where displacement is zero while distance is not? Explain.
6
Speed vs. Velocity
Speed ­­ scalar quantity which describes the rate of change in distance.
Mnemonic: speed & scalar start with the same letter.
Velocity ­­ is a vector quantity which describes a rate of change in displacement.
Mnemonic ­­ velocity & vector start with the same letter.
7
Determine the speed and velocity of the skier on each interval.
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9
Sally rides her bike 3 meters from point A to point B with the speed of 3 m/s (see picture). She then makes a 900 turn and rides for another 4 meters at a speed of 3 m/s.
3 1. What is the distance Sally travels?
2. What is Sally's displacement?
3. Is Sally's speed constant?
4. Is her velocity constant?
4 10
Acceleration
Acceleration is a vector quantity which describes the rate of change of velocity.
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1
Sally rides her bike from point 3 meters A to point B with the speed of 3 m/s (see picture). She then makes a 900 turn and rides for another 4 meters at a speed of 3 m/s.
Is Sally accelerating?
Yes
No
A 3 m B 4 m
C
12
Beth walks at a constant speed from point A to B, then to C, from C to D and then returns to A as shown on the picture below (assume all angles are 900).
A
4 m
B
3 m
D
C
Find:
1. Distance from A to C
2. Displacement from A to C
3. Total distance
4. Total displacement
5. Does Beth's speed change?
6. Does her velocity change?
7. Was Beth accelerating?
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Formula for Acceleration
ti
vi
v vf - vi
Δ
a= t = t
where
a -- acceleration
vi -- initial velocity
vf -- final velocity
t -- time
14
Use the formula and dimensional analysis method to derive the units for acceleration
15
General Procedure for solving word problems:
1. Write out what you know. Make sure to include a symbol, value and unit for each of the "knowns". Pay close attention to the information words in the problem (from rest, to stop, etc.)
2. Select and write down the equation(s)
3. Substitute values with units into the equation and solve.
4. List your finals answer as a value with a unit.
16
Find acceleration of the plane.
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1. Write out what you know. 2. Select and write down the equation(s)
3. Substitute values with units into the equation and solve.
4. List your finals answer as a value with a unit.
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1
Answer?
What is the acceleration of the race car?
19
What was the initial velocity of the car?
20
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Other Formulas for Constant (Uniform) Acceleration
22
What is the final velocity of the boat and the distance traveled by the boat?
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25
Calculate the minimum length of the runway. 2
Answer?
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