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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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