2-D positions, discplacement, velocity vectors

Day 1 Physics Final

speeding up

position, velocity, and acceleration should be in the same direction

slowing down

position, velocity, and acceleration not in the same direction

motion digram shows a snapshot of a particle at evenly spaced time intervals. is it speeding up or slowing down?

not enough information given

kinematics

motion

what quantities are important in describing motion of objects

direction of motion (x0 and xf)

scalar

quantity with only magnitude, no direction

\-can be positive, negative, or zero

Ex) 10 meters

vector

a quantity with magnitude and direction

\-typically expressed with an arrow

Ex) 10 meters north

1D vectors

\-one dimension (along a straight line)

\-only two directions (+/-) (up/down) (left/right)

2D vectors

magnitude and direction so set up on a coordinate plane (x&y)

position vector, r

points from the origin to the location of the object

r = (10m)x + (5m)y

unit vector x

is a dimensionless vector of unit length (1) pointing in the positive x direction

unit vector y

dimensionless vector of unit length (1) that points in the positive y direction

unit vectors specify direction

the have no dimensions or units Ax

Ax (usually)

Acos0

Ay (usually)

Asin0

direction formula

tan-1(Ay/Ax) = theta

Magnitude

sqrt(Ax^2 + Ay^2)

adding and subtracting vectors graphically

tip to tail method

* vectors can be moved to other locations without changing them, so long as their magnitude and direction are preserved

adding vectors using components

1. find the components of each vector to be added
2. add the x- and y- components separately
3. find the resultant vector using equation

negative of a vector

same magnitude pointing in the opposite direction

position is a

vector quantity -→ direction is important

origin does not have to be

the starting point

distance is a

scalar quantity and is always non-negative

scalars are

non negativevec

vectors are

positive, negative, or zero

displacement is the

change in position from one point to another

displacement is a

vector quantity -→ direction is important

displacement formula

final position - initial position (xf-xi)

displacement for a round trip

is zero

the displacement vector (delta r)

points from the initial position to the final position

average speed

the distance traveled divided by the time it took

average speed is a

scalar quantity

average speed formula

distance/elapsed time

average velocity is a

vector quantity

average velocity formula

displacement/time

unit: m/s

average velocity tells us

how fast something moves and the direction it is movingth

the average velocity of a round trip is

zero

speed vs velocity

speed is scalar and velocity is vector

slope of a line connecting tow points on a position vs time graph

is equal to the average velocity during the time interval

instantaneous velocity is given by the

slope of the tangent line at a given point

\-- derivative of position with respect to time

velocity tells us

how fast position changes with time

acceleration tells us

how fast velocity changes with time

units: m/s^2

average acceleration is given by the

slope between two points on velocity-time graph

instantaneous acceleration is given by the

slope of the tangent line at a certain point

each type of motion has a

the characteristic shape on a PT graph

Ex) zero speed, constant speed, accelerating, decelerating

zero speed graph

PT: straight line

VT: straight line on xaxis

AT: straight line on taxis

constant speed graph

PT: negative or positive slope

VT: straight line up/down

AT: straight line on axis bc no acceleration

accelerating/decelerating graph

PT: curved upward or downward

VT: positive or negative slope

AT: straight line up/down

area under velocity time graph

discplacement

kinematics equations only work under

constant acceleration

first kinematic equation

v(t) = V0 + at

second kinematic equation

x(t) = x0 + vot + 1/2at^2

third kinematic equation

vf^2 = vi^2 + 2a(deltax)

average velocity

1/2(vi+vf)

free falling objects

object is subject only to the influence of gravity

* acceleration is 9.81 m/s^2

free fall stops

the instant something else acts on the object

g is

always positive (acting towards the center of the earth)

\-9.81 m/s^2

an objects projected with an upward initial velocity

turning point is at the top and the velocity becomes zero and the object is momentarily at rest

object in free fall graphs

PT: parabolic

VT: cross axis

AT: negative (9.81)

projectile motion acceleration

ax= 0 m/s^2

ay= -9.81 m/s^2

which quantities are content during projectile motion

ax, ay, vx

projectile motion velocity

x component of velocity is constant and y component is changing