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- Descriptions of motion involve distance and speed, simple numbers w units called scalarsReference Frames: - Often represent reference frames as Cartesian or rectangular drawings Speed: - Can combine distance (change in position) and duration (change in time) to create a quantity called speed- Distance and duration are scalars, as well as speed- Speed is 0 if an object remains at rest - In m/s - Average speed = v = <v> = distance covered/duration of trip = d/ t△ △- Instantaneous speed: the value of speed at any point/instant in time- Can change and may not affect the average speed calculation - Not the same as <v>; as duration becomes small, the two become the same number Vectors: - Vectors carry 2 pieces of into; they contain magnitudes (scalars) and directions- Displacement combines the scalar distance with direction- Velocity combines the scalar speed with direction - We’ll deal with negative vectors. This doesn’t mean that the magnitude of the vector is negative, it refers to the direction- The vector a*arrow over pointing to right* has the same magnitude as the vector -a*arrow over pointing to right*- Tail -------------------------> head - Head ←--------------------- tail - Vectors are added head to tail; a + -(a) = 0- The result vector goes from the tail of the first to the head of the second Displacement: - a → ← -a- Distance covered = a- + distance covered = a- Total distance covered = 2a- Total displacement is 0Velocity:- Velocity vector points in the direction of the displacement vector - Need to take direction into account when calculating average velocity - During round-trip travel, your distance is not 0, but your displacement is, this makes the average speed and velocity differ Reading NotesAcceleration- Acceleration is the rate of change of velocity with time - An object accelerates whenever its velocity changes no matter what the change (increase or decrease) - Average acceleration is the change in velocity divided by the change in time - Aav = v/ t = v△ △ f - vi/tf - ti- SI unit: meter per second per second, m/s2- Instantaneous Acceleration- Vector- When acceleration is constant, the instantaneous and average accelerations are the same - Relating the Signs of Velocity and Acceleration to the Change in Speed - In one dimension, nonzero velocities and accelerations are either + or -, depending on whether they point in the positive or negative direction of the coordinate system chosen- Velocity and acceleration of an object may have the same or opposite signs- Two possibilities in one dimension:- When the velocity and acceleration of an object have the same sign, the speed of the object increases - When the velocity and acceleration of an object have opposite signs, the speed of an object decreases Lecture Kinematics Graphical Analysis- <v> = (final → pos - initial → pos)/(final time - initial time)- This expression is just that for the slope of a straight line, slope = rise/run - Average velocity is a slope, or rate of change Kinematics- Points to Take Away- Acceleration is a vector quantity that tells you how velocity changes with time - Just as position vs time plots Acceleration- A change in velocity with time - Not caused by velocity, and velocity is not caused by acceleration - Average acceleration is the slope of a velocity vs time curve- The instantaneous acceleration - What does it mean to have a negative acceleration? - Since tfinal is always larger than tinitial, it means that vfinal must be more negative than vinitial, 2.5-2.7 Notes Motion with Constant Acceleration- Aav = vf -vi/tf - ti = a- v - v0 = a(t-0) =atConstant-Acceleration Equation of Motion: Velocity as a Function of Time - v = v0 +at- Describes a straight line on a v-versus-t plot - Crosses the velocity axis at the value v0 and has a slope a, in agreement with the graphical interpretations discussed in section 2.4Position as a Function of Time and Velocity- x = x0 + vavtConstant-Acceleration Equation of Motion: Average Velocity- v(av) = ½ (v0 + v)- Acceleration isn’t constant Constant Acceleration Equation of Motion: Position as a Function of Time - x = x0 + ½ (v0 + v)tFreely Falling Objects- Motion with constant acceleration could be free fall - Objects of different weight fall with the same constant acceleration- Provided air resistance is small enough to be ignored Characteristics of Free Fall- If in free fall, it is assumed that an object’s motion is not influenced by any form of frictionor air resistance - Any motion under the influence of gravity alone - An object is in free fall as soon as it is released, whether it is dropped from rest, thrown downward, or thrown upward - Acceleration produced by gravity on the Earth’s surface is denoted with the symbol g - g = the acceleration due to gravity - g = 9.81 m/s^2 Lecture NotesLinear Motion- 1-D linear motion, dealing w vectors is easy; there is only one direction and motion is either in the + or - direction 3.1-3.4Scalars Versus Vectors - A scalar is a number with units. It can be +, -, or 0- Sometimes a direction is also needed, though - A vector is a mathematical quantity with both a magnitude and a direction- TO INDICATE A VECTOR WITH A WRITTEN SYMBOL, WE USE BOLDFACE FOR THE VECTOR ITSELF, WITH A SMALL ARROW ABOVE IT TO REMIND US OF ITS VECTOR NATURE, AND WE USE ITALICS TO INDICATE ITS MAGNITUDE Lecture Points to Take Away: - Motion in two dimensions can be broken down into two independent directions - Vectors have magnitudes and directions 2-D Reference Frames- In two dimensions, I need two numbers to specify the location of an object - Latitude and longitude- X and yVectors in 2-D- All the vectors that have been discussed behave the same way; displacement, velocity and acceleration - Any 2D vector can be broken down into an x-component and a y-component - How would you handle a 3D vector? Vector Arithmetic- Vectors can be added and subtracted 3.5-3.6- Position vector = Relative Velocity- We often define our reference frame to be the surface of the Earth- This means that we consider the surface of the EArth to be unmoving - We can always decide that we are the one that is not moving, and consider everything else (including the surface of the earth) to be moving - Our choice of reference frame cannot change reality- We could choose to follow the motion of a ball in free fall in a reference frame attached to the ball, but it wouldn’t change the fact that the ball encounters the surface of the

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