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# Physics Lecture Notes (Position &amp; Velocity Time Graphs) - magnitude of velocity vs velocity

Lecture Notes
(Position & Velocity Time Graphs)
Intro:
- in day-to-day usage, the terms speed and velocity are
interchangeable; in physics, however, there's a clear
distinction between them
- speed is a scalar quantity, having only magnitude, while velocity
is a vector, having both magnitude and direction
Speed:
- one of the most obvious characteristics of an object in motion is
how fast it is moving; this is an object's speed, v
speed, v distance (m)
time (s)
- speed is the rate at which distance is covered and is always
measured in terms of a unit of distance by a unit of time
- because objects do not always move at the same speed we often
use the average speed, v , of an object
- the average speed is the total distance traveled, divided by the
time required to cover the distance Ex. if a car travels 200 m
in 10 seconds, we say its average speed is 20 m/s
avg. speed, v total distance covered (m) , v d
time (s) t
- note that the symbol for average speed has a bar above it; do not
confuse this with the arrow over a symbol which stands for a
vector quantity
- because total distance and total time are always positive, the
average speed will be positive, also
- the unit of speed is m/s
Velocity:
- most people use the words speed and velocity interchangeably;
strictly speaking, however, there is a distinction between the
two
- when we say that something is traveling 60 km/hr we are
specifying its speed; however, when we say an object is
traveling 60 km/hr due north we are specifying its velocity
- when we describe speed andthe direction of motion, we are
specifying velocity, v or v ; the first symbol is bold faced
showing that this the vector quantity velocity and not the
scalar quantity speed
- average velocity is a vector quantity that points in the same
direction as the displacement of the object being studied; it is
the change in displacement divided by the time
- because displacement and velocity are both vector quantities,
they can be related in the same way that speed and distance
are related; time is a scalar quantity
avg. velocity, v displacement (m) , v d
time (s) t
- remember that the velocity can change during the time interval
Ex. in driving your car to Dallas, you may average 50 mph,
but that does not mean you are actually driving that speed the
entire time
- avvg. velociity does nnot reveall the veloccity for anny one mmoment off
time; thhe speed aand direction of ann object aat a particular
instant in time iss called thhe instanttaneous vvelocity
- innstantaneoous velocity is reprresented bby the syymbol v , with no
bar on ttop
- wwhen we saay that soomething is movinng at consstant velocity or
constannt speed, tthe we arre saying that the oobject is ccovering
equal ddistances iin equal iintervals oof time
- coonstant veelocity annd constannt speed ccan meann differentt things
- coonstant veelocity means consstant speeed with noo change in
directioon; Ex. aa car that rounds a curve at a constannt speed
does noot have a constant velocity, its velocity changges as its
directioon changees
Acccelerationn:
- gooing fromm place to place in your car,, you rareely travel long
distances at consstant veloocity; the velocity of the carr
increases when yyou step hharder onn the gas ppedal andd
decreasses when you applyy the brakkes

How do you find the magnitude of velocity? How to calculate instantaneous velocity from a position-time graph. Plot the displacement function with respect to time. ... Choose any two points on the s-t graph. ... Find the line slope connecting the two points, i.e., between A and B. ... Repeat to find slope several times, moving B nearer to A. ... Calculate the slope for an infinitely small interval on the tangent line. ...

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