PHYS 105 Acceleration and Velocity

for exam 1

acceleration vs. time graph

a graph of the velocity graph’s slope, where the horizontal axis represents time and the vertical axis represents acceleration; a downward spike on the graph = a decrease in velocity, while an upward spike on the graph = an increase in velocity

can instantaneous and average acceleration be equal?

yes, if acceleration is constant

finding instantaneous acceleration

calculate the average speed, over a short enough time that the speed does not change much, and then divide that by the short period of time

speed

the rate of change of distance from a starting/reference point; direction doesn’t matter; simply the rate of movement; how fast an object changes its location; the distance something travels divided by the elapsed time

velocity

comprised of speed/how fast an object is going (magnitude) AND the direction of that motion, such as 500 mph west; a vector quantity

average speed equation

total distance/total elapsed time; e.g., 140mi/2.6hr = 53.8 mph

instantaneous speed

what your speedometer tells you; exactly how fast you’re going at a given moment

vector quantity

has both magnitude, such as speed, and direction

change in velocity

can be a change in the object’s speed OR direction of motion OR both

acceleration

the rate of change in velocity over time; can be a change in speed OR in direction of motion; turning is acceleration

can a car accelerate even if speed is constant?

yes, because velocity also involves direction; therefore, even if one part of velocity stays the same, another part can still change meaning there will be acceleration (change in velocity)

instantaneous velocity

a vector quantity having a size (magnitude) equal to the instantaneous speed at a given instant in time, and a direction equal to the direction of motion at that instant

feeling velocity

not felt if velocity is constant

feeling acceleration

our bodies always feel it, such as a car changing speed or direction or an elevator speeding up or slowing down

can acceleration be zero even if velocity is non-zero?

yes, because a constant velocity is non-zero but also does not change, meaning there will be no acceleration

what is considered acceleration

ANY change in velocity, no matter if it is speeding up or slowing down

decrease in velocity

means acceleration is in the opposite direction of the velocity; not necessarily negative, depends on which direction you pick to be positive or negative; velocity values become less positive or more negative

direction of acceleration when velocity is increasing

acceleration is in the same direction as the velocity

delta symbolV

the change in velocity, aka acceleration

direction of acceleration for velocity at a constant speed with a change in direction

acceleration is at right angles to the velocity

direction of acceleration when velocity is decreasing

acceleration would be in the opposite direction as the velocity

average acceleration

the change in velocity divided by the time required to produce that change; a = deltaV/t, or change in velocity/elapsed time

example of average acceleration

a car accelerates to a velocity of 20 m/s due east in a time of 5 s: a = (20m/s)/(5s) = 4m/s²

instantaneous acceleration

acceleration at a precise instant in time; the rate at which velocity is changing at a given instant in time

how constant acceleration is depicted

depicted by a straight line, and unchanging slope, on a velocity vs time graph

uniform/constant acceleration

the simplest form of acceleration; occurs whenever there is a constant force acting on an object; most examples considered in this class will involve it; the acceleration does not change as motion proceeds

examples of uniform/constant acceleration

a falling rock or other falling object; a car speeding up at a constant rate while moving along a straight road

what the acceleration graph for uniform acceleration looks like

a horizontal line, because speed is changing but at a constant rate, meaning there is no change in acceleration

what the velocity graph looks like for uniform acceleration

a straight line with a constant slope, because while velocity is changing, the RATE of it is not changing; the slope is equal to the acceleration

equation for velocity

v = v0 + at, where v0 is the initial velocity, a is the acceleration, and t is the time

distance vs time (velocity) graph for uniform acceleration

has a constantly increasing slope, due to a constantly increasing velocity; the distance covered grows more and more rapidly with time

equation for distance at any given instant when you have velocity and time

multiple the velocity times the time at that instant, or d = vt

finding total distance covered when you have velocity and time

total distance covered is equal to the area under the graph

equation for final velocity

acceleration times time, or v= at

equation for average velocity when starting from rest

v = 1/2at, or avg velocity equals half of acceleration times time

equation for average acceleration from velocity and time

a = change in velocity/change in time, or a = Vf-Vi/change in t

what a negative slope on a distance graph means

means the distance is decreasing and therefore the object is moving in the opposite direction

what a negative slope on a velocity graph means

means that the speed is decreasing, or that the object is slowing down (when the speed is positive)

simplest type of motion

obviously, no motion; the object has no velocity, so it never moves, and the position of the object, relevant to a reference, is constant

uniform/constant motion

the next simplest type of motion; the object’s velocity does not change, so its position, relative to some reference, is proportional to time

how to find velocity from a distance vs time graph

velocity is equal to the slope of a distance vs time graph

effect of doubling the time interval for constant velocity

will result in a doubling of the object’s distance

slope of faster moving objects

faster moving objects will have steeper slopes on a graph than slower moving objects

when velocity is proportional to elapsed time

when acceleration is constant

equation for velocity when acceleration is constant and the object starts from rest

v = at

free fall

means gravity is the only thing changing an object’s motion; acceleration is constant

acceleration due to gravity

9.8m/s², ~10m/s² (also 22mph/s)

how fast an object will free fall

the velocity, so equal to acceleration times the time or at (v=at)

how far an object will free fall or travel

use the distance equation, so d = 1/2at²

slope of velocity vs time graph

the slope is the acceleration, so a = change in v/t

how to find the average speed for an object starting from rest

v = 1/2at

how to find distance for an object starting from rest

the same as the average speed times the time, or d = 1/2at²

curve of a graph for distance vs time with constant acceleration

the curve is not a straight line, since the distance is proportional to the square of the time (d=1/2at²)

you toss a ball straight upward in the positive direction. the ball falls freely under the influence of gravity. what is the velocity and acceleration at the highest point in the ball’s motion?

its velocity is zero (because it stops momentarily) and its acceleration is negative (downward, because velocity is decreasing/will be negative)

average velocity

equal to ½ the final velocity, or 1/2at

velocity for uniform acceleration

v = v0 + at, if initial velocity is 0, then it would simply be v = at

equation for average velocity for uniform acceleration

avg v = 1/2at

equation for distance for uniform acceleration

d = 1/2at²

g

acceleration due to gravity; ~10m/s²; a constant and downwards (negative); does NOT depend on weight

how far will an object fall in 4 seconds?

d = 1/2at², so d = 1/2(10)(4)² = 1/2(10)(16) = 1/2(160) = 80m

equation for velocity when throwing a ball down

must include the initial velocity, and therefore is v = v0 + at

equation for distance when throwing a ball down

must include the initial velocity, so therefore d = v0t + 1/2at²