Lesson 1.2 - Displacement and Velocity
By the end of this lesson, I will be able to:
Success Criteria:
By the end of this lesson, I can
VIDEO LESSON (45:41 min)
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RECALL
Displacement and velocity are vector quantities, i.e. they have magnitude and direction.
Displacement is the change in position, d, of an object with respect to a reference point in a given direction.
\( \Delta \vec{d} = 15m [W] \)
Velocity is the rate of change of position with respect to time.
\( \vec{v}=2.5m/s[Fwd]\)
Average velocity is the total displacement divided by time elapsed.
\(\vec{v}_{av}=\frac{\Delta \vec{d}}{\Delta t}\)
Watch Frames of Reference VIDEO (27:25 min)
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IN ONE DIMENSION
Once we define a frame of reference, we can just add vectors as if they were numbers.
EXAMPLE PROBLEM #1
A dog initially 4.3 m away from you runs 12 m further away to fetch a stick. How far away is the dog after it gets the stick.
SOLUTION:
What if the dog ran the other direction?
SOLUTION:
If the dog takes 0.4s, what are the velocities in each case?
SOLUTION:
IN TWO DIMENSIONS
Step 1: Draw a picture
Step 2: Define a coordinate system
Step 3: Break up each vector into components
Step 4: Add collinear components
Step 5: Use Pythagorean Theorem and Trigonometry to determine magnitude and direction of the resultant vector
EXAMPLE PROBLEM #2
A wide receiver first runs \(8.5 m [E]\), then \(13.2 m [N 32^o E] \) when the ball is snapped and then \(4.2 m [W]\) before being tackled.a) Determine the total distance travelled and the wide receiver's average speed if this takes \(6.4s\)
b) Determine the total displacement and the wide receiver's average velocity.
SOLUTION:
You can proceed to solve Problem Set 1.2 now. Below are more examples.
EXAMPLE PROBLEM #3
An airplane flies from Ottawa to Toronto, \(351 km [W 37^o S]\). Then it flies to Sault Ste. Marie, \(512 km [W 42^o N]\). Finally it flies to Churchill, Manitoba, \(1511 km [N 28^o W]\). What is the total displacement of the complete trip?SOLUTION:
EXAMPLE PROBLEM #4
The total displacement of two flight is \(1210km[E 15^o N]\). If the first flight is \(825km [E 40^o S]\), determine the displacement of the second flight.SOLUTION:
