1. Speed & Velocity

2. Linear Motion Linear motion: motion in a single dimension
Moving in a straight line
Ex: riding in a car without your hands on the steering wheel
Non-ex: making a turn around a corner

3. Rates Rate: A quantity divided by time
A rate tells how quickly something happens
miles per hour, words per minute, meters per second
Ex: speed (meters per second), acceleration (meters per second per second)
Non-ex: distance (meters), time (seconds)

4. Motion is Relative Frame of Reference: point of view of the observer
If something is relative, it depends on the frame of reference.
Usually, when we discuss the speeds of things on Earth, we mean the speed with respect to the Earth’s surface.

5. Speed Speed: the distance covered per unit of time.
Speed is a measure of how fast something is moving.
the rate at which distance is covered.
Speed: the distance covered per unit of time.
SI unit: m/s
Ex: 100 km/hr, 55 mph, 30 m/s
Equation: v = d / t
v = speed (m/s)
d = distance (m)
t = time (s)

6. Types of Speed Instantaneous speed Average speed
the speed at any given instant
Ex: speedometer; radar gun
Average speed
the total distance covered divided by the time
Average speed does not indicate changes in the speed that may take place during a trip.
BOTH instantaneous and average speeds indicate the rate at which distance is covered.

7. Physics Problem Solving Strategy
List your variables
Givens
Unknown variable
If need be, convert variables to SI units
Choose the equation that matches your variables
Substitute variables in to the equation
Solve

8. Check Your Understanding
If a cheetah can maintain a constant speed of 25 m/s, it covers 25 meters every second. At this rate, how far will it travel in 10 seconds?
d = ?
v = 25 m/s
t = 10 s
v = d /t
25 m/s = (d) / (10s)
d = (25 m/s)(10s)
d = 250m

9. Check Your Understanding
How about in one minute?
d = ?
v = 25 m/s
t = 60s
**Convert minutes  seconds**
v = d / t
25 m/s = (d) / (60s)
d = (25 m/s)(60s)
d = 1500m

10. Velocity Velocity: the speed in a given direction SI unit: m/s
Ex: 100 km/hr East, 55 mph North, 30 m/s Southwest
Equation: v = d / t
v = velocity (m/s)
d = distance (m)
t = time (s)

11. Speed vs Velocity
When we say that a car travels 60km/hr, we are indicating its speed. When we say that a car is traveling 60km/hr to the north, we are indicating its velocity.
Speed is a description of how fast an object moves; velocity is how fast it moves AND in what direction .

12. Check Your Understanding
The speedometer of a car moving northward reads 100 km/h. It passes another car that travels southward at 100 km/h. Do both have the same speed? Do they have the same velocity?
Both cars have the same speed, but they have opposite velocities because they are moving in opposite directions.

13. Types of Velocity Constant Velocity
requires both constant speed and constant direction (moving in a straight line)

14. Types of Velocity Changing Velocity 3 ways to change velocity
Increase speed
Decrease speed
Change direction
Constant speed and constant velocity are NOT the same thing.
Ex: A body may move with constant speed around a curved path, but it does not move with constant velocity b/c the direction changes at every instant.

15. Scalar Quantities Scalar: a quantity that requires magnitude only
Number and units ONLY; no direction
Ex: Speed, mass, time
Non-ex: Velocity

16. Vector Quantities
Vector: a quantity that requires both magnitude AND direction
Number, units, AND direction
Ex: Velocity, acceleration, force
Non-ex: Speed, temperature

17. Check Your Understanding
Is height a vector or a scalar quantity?
Scalar. Height only includes magnitude (how big the number is) only and NOT direction. You are 5’8” tall, not 5’8” to the east.

18. Vector Quantities
An arrow is used to represent the magnitude & direction of a vector quantity.
The length of the arrow indicates the magnitude (size) of the vector quantity.
The direction of the arrow represents the direction of the vector quantity.
10 m to the right
50 m to the left

19. Adding Vectors
When more than one vector combines together, both the magnitude AND the direction matter.
The sum of 2 or more vectors is called the resultant.
Draw the arrows tip to tail
The tail of the first arrow should be at the origin (at the beginning)
Place the tail of the next arrow at the tip of the first
The straight line from the tail of the first arrow to the tip of the last arrow is the resultant vector

20. + = Adding Vectors Arrows both point in the same direction
Draw the arrows tip to tail
The tail of the first arrow should be at the origin (at the beginning)
Place the tail of the next arrow at the tip of the first
Add together to find the resultant
Ex: 4 m/s E + 3 m/s E = 7 m/s E + =

21. + = Adding Vectors Arrows point in opposite directions
Draw the arrows tip to tail
The tail of the first arrow should be at the origin (at the beginning)
Place the tail of the next arrow at the tip of the first
Subtract to find the resultant
Ex: 4 m/s E - 3 m/s W = 1 m/s E + =

22. + = Adding Vectors When arrows are not in one dimension
Draw the arrows tip to tail
The tail of the first arrow should be at the origin (at the beginning)
Place the tail of the next arrow at the tip of the first
The straight line from the tail of the first arrow to the tip of the last arrow is the resultant + =

23. Example 1 + =

24. Example 1 + =

25. Example 2 + + =

26. Example 2 + + =

27. Example 2 + + =

28. Example 3 + + + + =

29. Example 3 + + + + =

30. Example 3 + + + + =

31. Example 3 + + + + =

32. Check Your Understanding
A boy is riding his bike down the street at a speed of 10 m/s. A gust of wind came out of nowhere headed towards the boy. If the wind is traveling 3 m/s, what will the boy’s new speed be?
Since the boy and the wind are moving in opposite directions, we need to subtract their speeds to find the resultant.
10 m/s – 3 m/s = 7 m/s

33. Position Time Graphs
Position Time graphs show the distance covered over an elapsed time
Aka Distance Time graphs and Displacement Time graphs
Time is always the independent variable
Position (distance) is always the dependent variable

34. Position Time Graphs
The slope of a Position-Time graph is equal to velocity
Slope = rise / run
Slope = position / time
Velocity = position / time

35. Position Time Graphs Slope of a position-time graph
The steeper the slope, the faster the velocity
A positive slope is forward motion
A negative slope is moving backwards
A zero slope is NOT moving at all

37. Check Your Understanding
Which person is moving faster, the red or blue jogger?
The red jogger. The red jogger’s line has a steeper slope and therefore a faster speed.

38. Check Your Understanding
Are both joggers moving forwards or backwards?
Forwards. The slope is positive, so the distance increases as the time increases.

39. Check Your Understanding
At what time does Person B pass Person A?
At 45 seconds. The lines intersect at this time and both runners are at the same position at the same time.