I: Intro to Kinematics: Motion in One Dimension AP Physics C Mrs. Coyle

Particle Model Position Vector Displacement, distance Average Velocity, Average Speed Instantaneous Velocity, Instantaneous Speed Intro to the Derivative. Graphical Analysis (position vs time) Uniform Linear Motion

Video Clip of Oil Spill in Gulf NPw0 NPw0

Motion Motion is relative Origin Position is compared to an origin Coordinate system or a reference frame

Motion Diagram t=0 sect=0.25 sec t=0.50 sec t=0.75 sec

Particle Model... t=0t=0.25s t=0.50s t=0.75s

Position Vectors Position (m) y=+4 m o x= -5m x= 5mx= 10 m

Position Vectors Position (m) o x=20mx=10m

Vectors and Scalars Scalars  Magnitude (size) Vectors  Magnitude and Direction

Displacement (  x): change in position.   x =x f - x i Position, x (m) o x 1 =15mx 2 =20m xx

Distance and Displacement Distance: (Scalar) Displacement  x =x f - x i (Vector)

Average Speed and Average Velocity Average Speed= Total Distance Travelled Time (Scalar) Average Velocity= Displacement =  x Time  t (Vector)

Prob. #2.4 A particle moves according to the equation x=10t 2 (x in meters, t in seconds). Find the average velocity for the time interval from 2s to 3s. Ans: 50m/s

Instantaneous Speed Instantaneous Velocity Instantaneous Speed  Speed at a given instant. (Time is very very small) Instantaneous Velocity  Velocity at a given instant. (Time is very very small) Instantaneous speed is the magnitude of instantaneous velocity.

Instantaneous Velocity: the limit of  x  as  t approaches 0.  t v = lim  x   t  0   t v = dx    dt

Instantaneous Velocity (or simply) Velocity is the derivative of x with respect to t. v = dx    dt

Instantaneous Velocity Instantaneous speed is the magnitude of instantaneous velocity.

Graphical Analysis of Motion Position vs Time Velocity vs Time Acceleration vs Time

Example 1: Graph of Position vs Time Time (s) o Position (m/s) Slope of Line= Average Velocity In this case does the slope also equal the instantaneous velocity?

Uniform Linear Motion Motion with constant velocity  Straight line  Same direction

Example 2: Graph of Position vs Time Time (s) o Position (m) Instantaneous Velocity at a given time= Slope of Tangent at that time

Example 2: Graph of Position vs Time Time (s) o Position (m) Find the instantaneous velocity at 2sec and the average velocity from 0 to 2sec

Example 3: Position vs Time Graph At what time(s) was the object at the origin? What is the average velocity from 0 to 1sec, 1 to 1.5 sec and 0 to 2sec? Time, (s) o Position, (m) A -10.0