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?

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 19.32. In which race did he run faster?

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

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

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”.

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.

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

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

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

Calculation USAIN! t v = 100m – 0 v = 200m – 0 Speed = Distance Elapsed Time s = d t 100m Race 200m Race v = 100m – 0 v = 200m – 0 9.63s– 0 19.32s– 0 v = 10.39m/s v = 10.32m/s How long would it take him to run 40yds? t = d s

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:

Graphical Interpretation of Average and Instantaneous Velocity

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

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

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

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

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

Average acceleration:

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

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

The relationship between position and time follows a characteristic curve.

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 = vo2 + 2ax 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)