1. Representing Motion Kinematics
…..in One Dimension
In the 2008 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 2008 Summer Olympics
In the 2008 Summer Olympics, Usain
Bolt won the 100 m race in 9.69s and
the 200m race in 19.3 s. 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 varible to identify distance is “x”.
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 “x”.

6. Speed and Velocity 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 “v”.
Average speed = Distance traveled
Time elapsed
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 “v”.
Average velocity = Displacement

7. 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

8. 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: Objects can accelerate by slowing down, speeding up or changing direction.
Acceleration = change in velocity
elapsed time

9. Acceleration and Deceleration
The (+/-) symbols indicate the direction of acceleration
A decelerating object represented as (-) and to the left
A accelerating object represented as (+) and to the right
Objects in motion will slow down whenever their acceleration and velocity are in opposite directions

10. 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)

11. Calculation USAIN! Δt tf - to v = 100m – 0 v = 200m – 0
Speed = Distance
Elapsed Time
v = Δx = xf – xo
Δt tf - to
100m Race 200m Race
v = 100m – v = 200m – 0
9.69s– s– 0
v = m/s v = m/s

12. Usain Bolt in the 40 yard Dash!
How long would it take him to run 40yds? t = x v
World Championship Records
200 m in 19.19s and 100 m in 9.58s