2 Kinematics describes motion in terms of Kinema is Greek for “motion”Kinematics → Describing motionKinematics describes motion in terms ofpositiondisplacementvelocity (average and instantaneous)accelerationDynamicsDescribing how interactions can change motionMechanicsKinematics and dynamics.
3 Position x is the location of the object initial positionfinal positionpositive x directionx axis at 0°For one-dimensional motion, plus (+) and minus (-) are used to specify the vector direction. Plus (+) is at 0° along the positive x axis and minus (-) is at 180° along the negative x axis.
4 Displacement Δx is the change in position Change Δ always means (final value) – (initial value)
5 Displacement is +5 m Example: Displacement in the positive x direction Displacement is the changeinitialfinalDisplacement is +5 m
6 Example: Displacement in the negative x direction initialfinalDisplacement is the changeDisplacement is - 5 m
7 Velocity is the displacement in one second. Average velocity is the displacement divided by the elapsedtime.v "bar" means averageSI units for velocity: meters per second
8 Example 2 The World’s Fastest Jet-Engine Car Andy Green in the car ThrustSSC set a world record of341.1 m/s in The driver makes two runs through the course, one in each direction, to adjust for wind effects. Determine the average velocity for each run.Vector directions are shown with +/- signs.
9 Ignore the textbook definition of speed In this course, speed will mean the magnitude of the velocity.SI units for speed: meters per second
10 Instantaneous velocity is the average velocity for a very short time interval. Average velocity is the average during some time interval.Instantaneous velocity is the velocity at a specific moment.
11 Average acceleration is the velocity change in one second. "bar" means average
12 Example 3 Increasing velocity: Determine the average acceleration. v and a are in the same direction so v increases
13 Acceleration is the velocity change each second. v and a are in the same direction so v increases
14 Acceleration is the velocity change each second v and a are in opposite directions so v decreases
15 Graphical representation of kinematic quantities Position graph with a constant slope
16 Position graph with three different slopes Velocity = Slope
17 Position graph with a variable slope Velocity = Slope
19 Your success in physics critically depends on your ability to correctly distinguish and correctly use technical terms as the terms are defined in physics.velocity and acceleration are different physical quantities with different unitsvelocity is position change each secondacceleration is velocity change each secondvelocity is different from velocity change
20 Five kinematic variables 1. position (at time t), x2. initial velocity (at time t=0), vo3. acceleration (constant), a4. final velocity (at time t), v5. final time, tThe kinematic equations relate these 5 variables for situations where the acceleration is constant and allow us to solve for two of these quantities that are unknown.
21 Five kinematic equations for constant acceleration cases Position equationsVelocity equationsObtained from the other equations by eliminating t.Use these equations to solve for any 2 missing variables.You need to know 3 of the 5 variables to find the missing 2 !Derivation of the kinematic equations is shown at the end of the slides.
22 Success Strategy [ Very important steps !! ] 1. Make a drawing. 2. Draw direction arrows. (displacement, velocity, acceleration) 3. Label the positive (+) and negative (-) directions.4. Label all know quantities.5. Use a table to organize known values with correct units.6. Make sure you have three of the five kinematic quantities.7. Select the appropriate equations and solve.There may be two possible answers because quadratic equations have 2 roots.For multi-segmented motion, remember that the final velocity of one segment is the initial velocity for the next segment.
23 x a v vo t Example: Find the final position x m s ? 8s same directions so v increasesFind the final position xxavvotms?8s
27 Free fall -- motion only influenced by gravity In the absence of air resistance, all bodies at the same location above the Earth fall vertically with the same acceleration. If the distance of the fall is small compared to the radius of the Earth, then the acceleration remains constant throughout the motion.This idealized motion is called free-fall and the accelerationof a freely falling body is called the acceleration due togravity. The direction of this acceleration is downward.The magnitude of the acceleration is called "g".
29 A stone is dropped from the top of a tall building A stone is dropped from the top of a tall building. What is the displacement y of the stone after 3 s of free fall?yavvotms?-9.8 m/s20 m/s3 s
30 Vertical velocity always momentarily zero at the top . A coin is tossed upward with an initial speed of 5 m/s. How high does the coin go above its release point? Ignore air resistance.Only one value is given in the wording of this problem. You are expected to add two values by thinking.Vertical velocity always momentarily zero at the top .yavvot?+5 m/s
32 The velocity changes, but does the acceleration change? Acceleration versus VelocityThere are three parts to the motion of the coin.On the way up, the vector velocity is upward and the vector acceleration is downward so the velocity change is downward (v gets less upward).At the top, the vector velocity is momentarily zero and the vector acceleration is downward so the velocity change is downward (v gets more downward).On the way down, the vector velocity is downward and the acceleration vector is downward so the velocity change is downward (v gets more downward).The velocity changes, but does the acceleration change?
35 multiply both sides by t Deriving the kinematic equationsWe assume the object is at the origin at time to = 0.andVelocity definitionmultiply both sides by tposition equationAlso, for constant acceleration cases
36 multiply both sides by t Acceleration definitionmultiply both sides by tVelocity equation