Understanding Acceleration: A Comprehensive Guide

good morning today today today today today we are going to discuss

acceleration so let's commence operations so for those of you following along in

your notes please turn to this page here average acceleration it's the ratio of

the change in velocity to time describes how quickly an object is changing its

velocity so there's our official formula for acceleration please fill that in your

notes delta v over delta t delta remember means

a change the unit for acceleration is meters per second per second

and notice because acceleration is a vector and that's what the symbol means it's a vector

involves velocity and velocity is a vector that means that a direction is required

one can show that meters per second per second is the same thing as meters per second squared

delta v what does it mean well it means the change in velocity where v2 is the final velocity and v1 is

the initial velocity now for there to be a change in velocity

either the speed of the object could change or the direction or both

so if we go back to this picture now a very famous basketball player dunking a ball in this

situation this person is undergoing acceleration why is that well at this point they're

probably running down the court and when they begin to leap

their direction is changing the person is going from a motion that is traveling him

forward to a motion that's traveling not only forward but upwards as well and so at that very moment

when he begins to lift off the court we say he is accelerating in addition what we'll learn in a future

video is that while he is in the air he is also accelerating due to the force of gravity that's for a

future video now let's say you were told that your car for example

has an acceleration of four meters per second per second what does that actually mean how would you explain that

to a child who doesn't understand the term acceleration what it means is this every second

if it was a car the speed of the car would increase by 4 meters per second that's what it means and if

you really understand that then you'll never need a formula to manipulate acceleration

questions and so imagine we have this car initially moving at 11 meters per second every second the speed of the

car increases by four meters per second so what does that mean

one second later what would the new speed of the car actually be without using any formula

just by using this simple understanding that every second the speed of the car increases by 4

meters per second well one second later be fifteen eleven plus four and

another second later what would it be nineteen fifteen plus 4. and another second later it would be

23. so simply by understanding what 4 meters per second per second means every second the speed

of the car increases by four meters per second you don't need a formula to figure out

simple analysis of the motion of a car so what does negative six meters per second

per second mean well it's the opposite if a positive means the car is speeding up in this case

the car would not be speeding up it would be slowing down we really don't use the term

deceleration in physics a car is always accelerating or an object is accelerating

whenever its speed or direction changes so in this situation if we say this car for example

has an acceleration of negative six notice i didn't use the term deceleration

we use the term acceleration physics whether it's speeding up or slowing down well if this car starts off at 18 meters

per second and every second the speed of the car decreases by six well

one second later its new speed would be 12. and another second later its new speed would be

six and of course another second later it would come to a stop here we have this picture in your notes

and you may be wondering how is this picture actually made

well here's the video happened so quick i'll show that to you again

it's a video of a car slowing down and essentially what we've done is we've removed images

if we play this video frame by frame and then extract these images and then put these images all together in one image

this is what we get so notice every 0.2 seconds i extracted one of the images

put them all together and this car specifically has constant acceleration and it's slowing down so the car slows

down and has constant acceleration and notice in one of these pictures what's happening to the gap

well notice the gap is getting smaller and smaller because the car is slowing down

until the gap is almost non-existent at the very end from one picture to the next

so this is what acceleration looks like when a car is slowing down let's see what it looks like when an

object is speeding up let's try it again so this rocket has an acceleration well

over 100 meters per second squared acceleration lasts for a very short amount of time

let's see if we can play it frame by frame and there we go ignition and notice

the gap from frame to frame is steadily increasing that's evidence that the object is speeding up

look at that gap small gap next picture the gap gets bigger from where the rocket was to where the

rocket is and that gap gets larger and larger sadly this rocket

well let's see what happened to this rocket six minutes later right there you can see it

it's just stuck in a couple of branches there's the rocket and just to give you an idea of how high this actually is

this is a tree and it must be a good well it must be a good

40 feet in the air oh wow you can actually see it in great detail

just where it's watched it'll come down by itself come on calm down come down

the rocket did not come down sadly let's look at our first example agent 001 jumps into his viper and immediately

guns it to forty kilometers an hour agent zero zero one follows all speed limits and motor

vehicle laws if the average acceleration is seven meters per second squared which is

seven meters per second per second how long does it take zero zero one to reach that speed

let's see so our goal is to get time well this really isn't indicating the

problem however one can assume that when agent001 enters a car the initial speed of that car would be zero

so we denote that as v1 the one standing for initial the final speed is 40

kilometers per hour and immediately you may identify this problem here we have the

unit kilometers per hour however the acceleration is in meters per second squared

that's an issue and so in the previous video we discussed converting kilometers per hour

into meters per second and the magic factor was 3.6 and so when we divide by 3.6

this is this final speed in meters per second remember that v2 the 2 stands for final

speed here's our acceleration of 7 meters per second per second

which is the same thing as 7 meters per second squared and so we're going to use this formula

here go ahead give it a try now well let's see how we work through with

this formula we substitute our values 7 goes for acceleration

the final speed is 11 and the initial speed is 0. we cross multiply our delta t 7 delta t

equals 11.1 and then we divide if we consider significant digits

the answer is two seconds with significant digits now does this make sense 1.6 seconds or

2 seconds does it actually make sense well recall that every one second its speed increases

by seven so at zero seconds it's zero one second later it'd be seven two seconds later seven plus 7 would be

14 so it does make sense because the car only has to hit 11.1

meters per second not 14 meters per second example two two cars are initially

traveling at 25 meters per second both cars apply their brakes and come to a stop a dodge stealth coast to a stop

in 20 seconds whereas a g37 rapidly comes to a stop in four seconds calculate the

acceleration for each car go ahead pause the video now try this out

okay hopefully you tried that so for the stealth we know the time we know the initial speed is 25 meters

per second that's called v1 and of course the object is coming to a stop

that's the final speed that's v2 so we're solving for acceleration here and here's our formula for that

we're going to substitute our numbers final speed is zero initial speed is 25 and we're dividing

by 20. and we get an answer of negative 1.25 meters per second squared

or with significant digits only negative 1. the negative should make sense whenever

an object is coming to a stop or slowing down typically the acceleration

is a negative acceleration go ahead try the g37 for yourself repeat the exact same steps

with the exception that the time is not 20 seconds it's only 4 seconds for the g37

let's look at example 3. a car accelerates for four thousand milliseconds and has a final speed of 72

kilometers per hour calculate the initial speed prior to accelerating

please pause the video and try this out all right hopefully you tried this question

here's the solution time i always like to give my students time in units other than seconds

you have to be aware of converting the units in this case four thousand milliseconds

is four seconds because remember one thousand milliseconds is one second we're looking for the initial speed

that's v1 once again i give you a speed that's not in meters per second in kilometers per

hour and we have to convert so that our units are consistent

20 meters per second is the final speed here which is 72 kilometers an hour and we're given our acceleration which is 3

meters per second per second or 3 meters per second squared well substituting our numbers and then

remembering we have a 4 here we're going to cross multiply that 4. 3 times 4 equals 20 minus v1

we're trying to get the initial speed 12 equals 20 minus v1 and sometimes students get all

mixed up with solving this equation but remember every equation tells a story and this equation is no different it's

saying that 20 subtract a number is equal to 12.

well we all know that what that number has to be 20 subtract 8 equals 12. so just look at the equation

and ask yourself what's the story it's telling us because i sometimes see students make

errors at this point if you just understand what the equation is telling us

you can reason what the answer will be the answer is eight meters per second when you rearrange the formula

and so hope you have a great day bye bye