PHYS 105 Ch 2 Reading Notes

for exam 1

speed

how fast something is moving without regard to direction of motion - not a synonym for velocity

average speed

distance traveled divided by the time traveled; the rate at which distance is covered over time; s = d/t; says little about variation in speed, but tells you how long a trip might take

rate

one quantity divided by another, especially a quantity divided by time; rates of time, like miles per hour and meters per second, are important in measuring motion

time rates

the quantity that divide by is time, such as with average speed (s=d/t)

instantaneous speed

how fast an object is moving at a particular instant; related to average speed for very short time intervals; tells us little about how long it will take to travel several miles, unless the speed is held constant

velocity

a vector quantity that describes how fast an object is moving AND the direction it is moving; speed plus a direction (70 mph east)

magnitude

the size of something expressed as a quantity; the magnitude for velocity is how fast something is going

vectors

a quantity that has both magnitude and direction, often represented by an arrow; the length of the arrow is proportional to the size of the vector quantity, and the angle shows its direction

vector quantity

any quantity, such as velocity or a force, for which both the size and the direction are needed for a complete description

instantaneous velocity

a vector quantity that is made up of an object’s instantaneous speed and its direction at that instant

acceleration

the rate of change of velocity

average acceleration

the rate of change of velocity over time, or deltav/t

units for acceleration

m/s², or meters per second per second

instantaneous acceleration

the rate at which velocity is changing at a given instant in time; found by finding the average acceleration for a very short time during which the acceleration does not change appreciably

direction of acceleration

that of the change in velocity; think, if a car is slowing down, something must be pushing backward on it

when velocity is decreasing

the velocity and acceleration vectors point in opposite directions and therefore have opposite signs

when velocity is increasing

velocity and acceleration vectors point in the same direction and have the same sign

is a car turning at a constant speed accelerating?

yes, because even though the magnitude of velocity isn’t changing, the direction is

slope of distance vs time graph

at any point is equal to the instantaneous velocity of the object; if the slope is constant, then the velocity is constant; velocity changes only where the slope changes

how to tell if slope is constant

any straight-line segment of a graph has constant slope

slope of velocity vs time graph

equal to the instantaneous acceleration; a steep slope represents a rapid change in velocity and thus a large acceleration, while a horizontal line represents no change in velocity and thus 0 acceleration

distance traveled for velocity vs time graph

equal to the area under the velocity vs time curve

negative velocity

means the object is traveling backward

uniform acceleration

acceleration with a constant rate of change in velocity, the simplest kind of accelerated motion; has a horizontal graph

equation for velocity at any time

v = v0 + at

equation for change in velocity

deltav = at