1. Representing Motion Kinematics
…..in One Dimension
In the 2012 Olympics, did Usain Bolt run faster in 200m or the 100m?
If he ran at his fastest average speed,
how fast could he run 40yards?

2. Usain Bolt 2012 Summer Olympics
In the 2012
Summer Olympics, Usain
Bolt won the 100 m race in 9.63s and the 200m race in In which race did he run faster?

3. Kienematics in One Dimension
Mechanics- The branch of physics that focuses on the motion of objects and the forces that cause motion to change
Two Parts to Mechanics
Kinematics Describe motion without any reference to the forces that cause motion
Dynamics describe the effect that forces have on motion

4. Review: Scalars and Vectors
Scalars are measurements that are described by a magnitude (size) only they do NOT include a direction.
Examples: Time & Temperature
Vectors are measurements that require a magnitude and direction to completely describe the value.
Example: The train traveled at 15 m/s, due east

5. Distance vs. Displacement
How far something travels.
It is a scalar quantity. It has magnitude only. (no direction)
SI unit is the meter (m)
The variable to identify distance is “d”.
Displacement
How far something travels in a given direction.
It is a vector quantity that has magnitude and direction.
SI unit is also the meter (m)
The variable to identify displacement is also “Dx”.

6. Position, Distance, and Displacement
Displacement is the change in position. If you drive from your house to the grocery store and then to your friend’s house, your displacement is 2.1 mi and the distance you have traveled is 10.7 mi.

7. Create a Variable Table for each unit on a portion of the Memory Aides Page
Name
Symbol
Define
Equation

8. Speed and Velocity Create a T Chart to compare contrast s and v
Speed is how fast something is moving.
It is a scalar quantity. It has magnitude only. (no direction)
SI unit is the meter/second
The variable to identify speed is “s”.
Average speed = Distance traveled = Δd
Time elapsed = Δt
Velocity is how fast something is moving in a given direction.
It is a vector quantity that has magnitude and direction.
SI unit is also the meter (meter/second)
The variable to identify displacement is also “d”.
Average velocity = Displacement = Δd with direction
Time elapsed = Δt

9. If you return to your starting point, your average velocity is zero

10. Calculation USAIN! t v = 100m – 0 v = 200m – 0
Speed = Distance
Elapsed Time
s = d t
100m Race 200m Race
v = 100m – v = 200m – 0
9.63s– s– 0
v = 10.39m/s v = 10.32m/s
How long would it take him to run 40yds? t = d s

11. The same motion, plotted one-dimensionally and as an x-t graph:
Graphical Interpretation of Average Velocity
The same motion, plotted
one-dimensionally and as an
x-t graph:

12. Graphical Interpretation of Average and Instantaneous Velocity

13. Instantaneous Speed and Velocity
Instantaneous speed: The speed at instant.
Instantaneous velocity is speed in a given direction.
Example: Your speedometer reading.
Time
SI Unit for Time is the second (s)
Time Interval = Dt = tf – to
= final time – initial time
The symbol Δ is called Delta which means “change in”
Timing measurements usually start at time zero, but actually may be measured at any moment of motion

14. Acceleration
The rate at which the velocity changes during a given amount of time. It is a vector.
Units are m/s2
Variable “a”
Examples: 11 m/s2
Acceleration = change in velocity
elapsed time

15. Acceleration There are 3 ways an object can accelerate:
Speeding up (accelerating)
Slowing down (decelerating)
Changing direction (moving in a circle)

16. Acceleration (increasing speed) and deceleration (decreasing speed) should not be confused with the directions of velocity and acceleration:

17. Acceleration and Deceleration
The (+/-) symbols indicate the direction of acceleration
(-) South, down, West and to the left
(+) North, up, East and to the right
Objects in motion will slow down whenever their acceleration and velocity are in opposite directions

18. Average acceleration:

19. If the acceleration is constant, the velocity changes linearly:
Average velocity:

20. Average velocity:
Position as a function of time:
Velocity as a function of position:

21. The relationship between position and time follows a characteristic curve.

22. Kinematic Equations v = x/t Dt = tf - to vf = vo + at
Constant Velocity
(no acceleration, a = 0)
v = x/t
v = Δx = xf – xo
Δt tf - to
Dt = tf - to
Acceleration
vf = vo + at
x = 1/2 (vo + vf)t
x = vot + 1/2at2
vf2 = vo ax
vo = initial speed or velocity – units (m/s)
vf = final speed or velocity – units (m/s)
xo = initial position – units (m)
xf = final position – units (m)
t = time – units (s)
a = acceleration – units (m/s2)