Kinematics – the study of the motion of objects without consideration to mass or the forces acting upon objects.

Is the circle in motion?

Scalars and Vectors Scalar – any quantity that measures only magnitude (amount) Ex. 4.0 kg, 53 seconds, 25 students Vector – any quantity that shows both magnitude and direction Ex. 6.3 m/s, east; 9.2 N, 53° ; -12 m/s One dimensional vector conventions: +: right, east, north, up - : left, west, south, down

Frame of Reference – a defined system used to determine the motion of an object. Reference point – a single location in the frame of reference to compare motion (origin) Position – the location of an object in a given reference frame with respect to the reference point. Position is a vector (magnitude and direction) quantity. position = direction and magnitude position = +/- (distance from reference) m +20.0m m m +50.0m Defining Motion Terms What is the position of this jogger?

m Why is direction important? reference

m +10.0m m m +25.0m What is the position of these joggers? m m 0 m m m m

Displacement Change of position in a straight line path. A vector quantity Displacement=magnitude and direction Displacement = +/- distance Denoted by Δd (Δp) ∆d= Δp = p 2 -p 1 Straight line change in position (meters) Displacement

What is the displacement of the jogger? From the start Δd=Δp=p 2 - p 1 =+50.0 m – (0 m) =+50.0 m =+50.0 m Between the end of the first portion of the trip to the second location Δd=Δp=p 2 - p 1 =+50.0 m – (+70.0 m) = m = m

Distance Scalar quantity Length of the path traveled Length of separation between two locations The magnitude of displacement is distance. Distance=|Displacement| (straight line path)

What is the distance traveled by the jogger? d = 70.0 m m = 90.0 m What is the distance of the jogger from the starting location? 50.0 m What distance does the jogger travel after turning around? 20.0 m

Speed Speed = distance/time The SI unit of speed is m/s Instantaneous speed the exact speed at a specific point in time. Average speed - the speed taking into account changes in motion Speed is a scalar quantity. Speed – rate of motion (distance traveled per unit time) 200 km/hr

Velocity A vector quantity Speed with direction (+/- speed) Ex: +3.7 m/s; -8.2 m/s; 33 km/hr, north, 200 km/hr at 15°E of N v = Δd/Δt=Δp/Δt=displacement/time=(p 2 -p 1 )/(t 2 -t 1 ) The SI unit for velocity is m/s. Instantaneous velocity – the velocity at a specific time Average velocity – the velocity that takes into account changes in motion Velocity is a straight line change in position of an object per unit time. Speed is the magnitude of velocity (straight line motion) Speed = |velocity| (straight line motion) 200 km/hr, NNE

Uniform Motion Equations displacement=change in position Δd = Δp = p 2 – p 1 Δd = Δp = p 2 – p 1 velocity = displacement / time Speed = distance/time s = d/t s = d/t

m m +300m +400.m m +600.m +700.m +800.m Let each second equal one minute. STOP Situation 1 START

meters STOP Situation 2 START

Motion Calculations 1. What are the starting and final position of the jogger, respectively? 2. What is the distance traveled by the jogger? 3. What is the displacement of the jogger from the start? 4. What is the average speed of the jogger? 5. What is the average velocity of the jogger? For each situation:

Question Answers Situation 1 Situation 2 TimeDistanceTimeDistance Question # min =1030 s m s 23.0 m 1. 0, m, +1.0 m m 23.0 m 3. 0 m -3.0 m m/s 1.64 m/s 5. 0 m/s m/s

Questions to Consider Why is the speed an average? Why is the velocity between beginning and end an average? What is the interpretation of having an average velocity of m/s in the second situation? (-0.21 m/s)(14 s) = -3.0 m =displacement startend

Average Velocity If the velocity of an object changes uniformly, then the average velocity can be found by: vivi vfvf v t Vel vs Time v avg