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?

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?

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 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”.

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

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

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

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)

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 – 0 v = 200m – 0 9.69s– 0 19.3s– 0 v = 10.3199m/s v = 10.3626m/s

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