1. Introduction to Kinematics
Vectors, Scalars, and Motion!

2. Vector vs. Scalar Quantities
Only has magnitude
Vector Quantities:
Have magnitude AND direction
Represented with an arrow
+ or – indicates the direction

3. Distance vs. Displacement
Distance (Scalar)
How far you have travelled
Displacement (Vector)
How far you are from your starting point
+ or – indicates direction

4. Let’s Practice! REMEMBER: “Distance” is how far you have gone
“Displacement” is how far you are from the starting point
Distance = 1 m
Displacement = + 1 m
Distance = 3 m
Displacement = - 1 m
Start
1 meter
-1 meter
Distance = 2 m
Displacement = 0 m
Distance = 4 m
Displacement = 0 m

5. Speed vs. Velocity Speed (Scalar) Velocity (Vector)
How fast an object is moving
More precisely, it’s the rate at which an object covers distance
Velocity (Vector)
The rate at which an object changes its position (displacement!)
+ or – indicates direction

6. More About Velocity
Average Velocity: the overall displacement covered in a given time period
Units = m/s = m·s-1
*Note: average speed = total distance per unit time
Instantaneous Velocity: The speed and direction of a moving object at a particular instant in time
Initial velocity  v 1 (or v i or v o)
Final velocity  v 2 (or v f or v )

7. Let’s Practice! REMEMBER: “Speed” is how fast you go
“Velocity” is how fast in a given direction
Speed = 3 m ÷ 3 s = 1 m/s
Avg. Velocity = - 1 m ÷ 3 s = m/s
Speed = 1 m ÷ 1 s = 1 m/s
Avg. Velocity = + 1 m ÷ 1 s = + 1 m/s
Start
1 metre
-1 metre
Speed = 2 m ÷ 2 s = 1 m/s
Avg. Velocity = 0 m ÷ 2 s = 0 m/s
Speed = 4 m ÷ 4 s = 1 m/s
Avg. Velocity = 0 m ÷ 4 s = 0 m/s

8. Acceleration Acceleration (Vector): ANY change in velocity
Speeding up (final velocity is a larger magnitude than the initial velocity)
Slowing down (final velocity is a smaller magnitude than the initial velocity)
Changing directions (the direction of the vector is changing)
Average Acceleration: the rate at which velocity is changing
Units = m/s2 = m·s-2

9. Speeding up Slowing down Positive velocity, positive accelerationOR
Negative velocity, negative acceleration
Speeding up occurs when velocity and acceleration are in the same direction
Slowing down
Positive velocity, negative acceleration
Negative velocity, positive acceleration
Slowing down occurs when velocity and acceleration are in the opposite direction.

10. Setting coordinate system
Determine which direction is the positive direction and which is the negative direction.
Traditionally, the positive direction is up or right, but as long as you’re consistent within the problem, it is up to you.
Determine which quantities in the problem are vectors and draw vector arrows in your diagram representing their relative size and direction

11. Problem Solving Strategy
Sketch the problem
Determine the + direction; decide on a “0” position
Diagram the scenario, labeling known & unknown variables
What do you know?
List all known variables including units (some given, some conceptual)
What do you want to know?
List any unknown variables – what is the question asking you to find?
List the appropriate equation in variable form
If necessary, rearrange the equation and show mid-steps Plug and chug
Insert all known quantities, including units; calculate your answer.
Final answer with appropriate units and sig figs
Double check your work

12. Scalar or Vector? Scalar Vector 1. Mass 2. Distance 3. Displacement
REMEMBER:
Scalar quantities have size only and no direction.
Vector quantities have both size and direction.
Scalar
Vector
1. Mass
2. Distance
3. Displacement
4. Speed
5. Velocity
6. Energy
7. Time
8. Power
9. Momentum
10. Acceleration
11. Force

13. Practice Problems (do these in your journal!)
Josie jogs around a 400m track around the football field. It takes her 80s to complete a lap
What is Josie’s distance after 1 lap? Displacement?
What is her speed after 1 lap? Average velocity?
A dog runs +5m to get a ball. He then turns around at runs 2m back to his owner. What distance did he run? What is his displacement?
A car travels +20.0m in 2.0s. It then backs up 4.0m in 1.0s. What is the average velocity of the car? Speed?
A car accelerates from +8.0 m/s to m/s in 3.0s. Find it’s acceleration.
Find the acceleration of a motorcycle that slows down from 18 m/s to 0.0 m/s in 6.0s.

14. Practice Problems SOLUTION
Josie jogs around a 400m track around the football field. It takes her 80s to complete a lap
What is Josie’s distance after 1 lap? Displacement?0
What is her speed after 1 lap? Average velocity?
s in 6.0s.

15. Practice Problems SOLUTION
A dog runs +5m to get a ball. He then turns around at runs 2m back to his owner. What distance did he run? What is his displacement?
of a motorcycle that slows down from 18 m/s to 0.0 m/s in 6.0s.

16. Practice Problems SOLUTION
A car travels +20.0m in 2.0s. It then backs up 4.0m in 1.0s. What is the average velocity of the car? Speed?
of a motorcycle that slows down from 18 m/s to 0.0 m/s in 6.0s.

17. Practice Problems SOLUTION
A car accelerates from +8.0 m/s to m/s in 3.0s. Find it’s acceleration. acceleration of a motorcycle that slows down from 18 m/s to 0.0 m/s in 6.0s.

18. Practice Problems SOLUTION
Find the acceleration of a motorcycle that slows down from 18 m/s to 0.0 m/s in 6.0s.