1. VELOCITY AND ACCELERATION NOTES
Physics

2. On the set of ten problems, circle the quantities that represent SCALARS

3. DEFINITIONS AND VARIABLES

4. QUANTITY an measured numerical value
ALWAYS includes both a number and a unit
examples: 10 m, 35 s, 45 km/h
all quantities in science are represented by a variable in equations
examples
distance has the variable symbol, d
velocity has the variable symbol, v
NOTE: It is crucial to your success in physics to know what the units for different quantities are as well as their variable symbols!!!

5. TYPES OF QUANTITIES Vector quantities Scalar quantities
quantities that have only magnitude (amount)
examples: distance, time, speed
Vector quantities
quantities that not only have a magnitude but also include a direction
examples: velocity, acceleration, force
any quantity calculated using a vector quantity is itself a vector quantity
direction is included in quantity, ex. 10 m, N (10 meters, North)

6. DISTANCE VS. DISPLACEMENT
Distance = how far an object has moved
scalar
does not matter what direction object moved
Displacement = how far an object has moved in comparison to a starting point (reference point)
vector
only concerned with where the object is from the starting point – not how far it traveled in total

7. SPEED VS. VELOCITY Speed = how fast an object moves
scalar
Velocity = the speed of an object as it moves in a particular direction
vector
two objects can have the same speed but not the same velocity if they travel in different directions

8. ACCELERATION
the rate at which the velocity of an object changes over time
vector

9. VARIABLE SYMBOLS AND UNITS
distance, displacement
variable: d, D
units: m, km, mi
speed, velocity
variable: s, v
units: m/s, km/h, mph
acceleration
variable: a
unit: m/s/s OR m/s2

10. MOTION GRAPHS

11. DISPLACEMENT VS. TIME GRAPHS
show how the object’s position is changing over time
x-axis: time (s)
y-axis: displacement (m)
slope of line = velocity (m/s)
Next three slides show various types of velocity

12. ZERO VELOCITY
at every point in time, the object is at the same displacement
object is NOT moving
remember slope of horizontal line = zero

13. CONSTANT VELOCITY
at every point in time, the object has moved an equal distance
object is moving at a constant rate
graph shows uniform motion

14. CHANGING VELOCITY
velocity of object is increasing at every point in time
changing velocity = acceleration, so object has constant acceleration

15. VELOCITY VS. TIME GRAPHS
show how the object’s velocity is changing over time
x-axis: time (s)
y-axis: velocity (m/s)
slope of line = acceleration (m/s/s OR m/s2)
Next three slides show various types of acceleration

16. ZERO ACCELERATION
at every point in time object moves with the same velocity
object is moving at a constant velocity (slope of line = zero, so zero acceleration)

17. CONSTANT ACCELERATION
object moves at an increasing velocity at every point in time
object’s velocity is increasing at a constant rate

18. CHANGING ACCELERATION
at every point in time, the object’s velocity is increasing at a faster and faster rate
graph shows increasing acceleration

19. ACCELERATION VS. TIME GRAPHS
show how the object’s acceleration is changing over time
x-axis: time (s)
y-axis: acceleration (m/s/s OR m/s2)
not used as frequently as displacement- time graphs and velocity-time graphs
Next two slides show constant and changing acceleration

20. CONSTANT ACCELERATION
at every point in time the object’s acceleration is the same
zero slope shows constant acceleration

21. CHANGING ACCELERATION
at every point in time, the object’s acceleration increases at a constant rate
graph shows constantly increasing acceleration

22. ALL CONSTANT VELOCITY GRAPHS (ZERO ACCELERATION)

23. ALL CONSTANT ACCELERATION GRAPHS

24. DISPLACEMENT FROM VELOCITY TIME GRAPHS

25. CALCULATING DISPLACEMENT FROM A VELOCITY-TIME GRAPH
the area under the line of the graph = displacement
x-axis is time while y-axis is velocity, so multiplying velocity by time gives displacement (d = vt)
area calculations:
rectangle or square: A = l x w
triangle: A = ½ bh

26. EXAMPLE ONE What is the displacement of the object in the first 6 s?
Shade in area under line for first 6 s
area = ½ bh
area = ½ (6)(30)
area = 90 m

27. EXAMPLE TWO How far does the object travel between 6 s and 14 s?
Shade in the area under the line between 6 s and 14 s
area = l x w
area = (14-6)(30)
area = (8)(30)
area = 240 m