Sign Convention & Direction
Motion has a 1) Direction2) Magnitude - How much motion has or is occurring
Positive: Up, to the right, North, to the EastNegative: Down, to the left, South, to the West
Sign Convention & Direction
Motion has a 1) Direction2) Magnitude Needs a frame of reference, an origin to definepositions at different times.
Requires changes in TIMEUniform Motion means a time intervals are the same
Distance & Displacement
Distance (x) equates
Displacement equates to Difference between initial xi and final xf .
x is position from the reference
A person moves on the number line shown below. The person begins at B, walks to C, and then turns around and walks to A. For this entire range of motion DETERMINE: a)the person’s final positionb)the displacementc)the distance.
Example
0 5 m 10 m 15 m
A B C
Speed & Velocity
Speed: How far
Velocity: How
Speed: distance traveled time interval
Speed and Direction
Velocity = x t
EXAMPLEUsain Bolt holds the record for the 100m sprint completing it in only 9.58s!
a) Determine his average speed in m/s. (1.6km = 1mi)
b) Mr Sample (I hold no record) ran the Philly half-marathon (13.1mi) in 1hr55min36sec. Determine my avg speed in mph.
Did he run faster than this at some point?
Vectors
Go East then go West
What is the final displacement? (this is
a vector)
What is the distance traveled?
5 mi 3 mi
Vectors
Go East then go South
What is the final displacement? (this is
a vector)
What is the distance traveled?
4 mi 3 mi
Vector Notation
• Vector A A
• A + B This adds the 2 vectors
• Vectors do not have to be in the same
Direction to be added.
See page 19 in textbook
Vectors and Trig
Were A, B, and C are vectors (magnitude and direction)
•sin Θ = A/C
•cos Θ = B/C
•tan Θ = A/B
A commuter drives 15.0km on the highway at a speed of 25.0m/s, parks at work and walks 150m at a speed of 1.50m/s from his car to his office.
Example
b) Determine the average speed of the entire commute
(a) Determine the total time of the commute.
Example: A woman starts at the entrance to a mall and walks inside for 185m north for 10minutes. She then walks 59m south in 3minutes to another store. She then leaves the store and moves south 155m in 8minutes to reach her car outside.Determine her average velocity during the trip.
Instantaneous Velocity
The instantaneous speed or velocity is how fast an object is moving at a single point in time.
Does the gauge on your dashboard give you speed or velocity?
Does this gauge give you an average or instantaneous value?