Understanding Kinematics: Constant Velocity and Acceleration

good morning today today today today today we're going to continue with our investigation of

kinematics and specifically we're going to be using the kinematic equations

to do an experiment a little later on so let's commence operations

for those of you following along in your notes please turn to this page now when object is moving at constant

velocity the formula used to determine time or displacement is

displacement over time or in the case of speed distance over time that's something we

already reviewed in the previous videos however when an object moves with

constant acceleration we have five formulas here are the five formulas that we could

potentially use please note you can only use any of these formulas

when we have constant acceleration delta d of course represents displacement

v1 represents initial velocity v2 represents final velocity and a represents acceleration and t

represents time to use any one of these five equations any one of these five equations we

always need three variables so it's important that before you begin to try to use any of these equations

you have to determine what your three variables are now if you're taking another course for

example an ib physics course these would be the symbols used

for those five equations s here represents displacement v represents the final velocity and u

represents the initial velocity and of course a still represents acceleration and t still represents time

so the equations are the same the symbols are slightly different all right let's look at a common example

a student is going to be late oh no for her class so instead of walking she puts on

her inline skates and blades the school the student is initially stationary and in 5500 milliseconds has moved 15 meters

and the e here stands for east what is the final velocity of the bleeder so this is a classic problem in

kinematics where we have to apply one of those equations the other assumption that i

didn't mention yet is that it's important to consider that all the motion has to be in one

direction so for example this person truly would have to have moved 15 meters

east effectively and not moved north or south while moving east so in other words they're traveling

in a line so we're told the time and 5500 milliseconds that's not a good unit

to use we need seconds so recall that a thousand

milliseconds is one second so that's 5.5 seconds we're told the initial speed it's zero

the student is initially stationary that means the initial speed is zero and remember there needs to be one more

variable well the final variable is displacement 15 meters

we don't have to write 50 meters east because a positive 15 implies east

our goal is to get the final speed which is v2 so here are our equations and there's

five of them in total but only one of them is going to work the equation that we're looking for has

to have time in it has to have initial speed has to have final speed and of course displacement

so which equation has those four variables in it well it's not this one this one's got an

a and there's no a here it's not that one either that one has acceleration and again

there's no acceleration here can't be this one again that has acceleration and we don't

have acceleration here and it can't be that one because again this equation has acceleration and we

don't have acceleration here and so it's this one here delta d equals half v1 plus v2

times delta t okay so we're going to use this equation right now and substitute

these numbers into the formula and so 15 being our displacement it's equal to half zero is our initial

speed and our time is 5.5 seconds now there's many different ways of mathematically solving this i'm going to

show you what i think is easiest way half times 5.5 is 2.75 and then we take our 15 and divide by

2.75 and we end up with this answer here and there's our final velocity in significant digits it would be 5.5

meters per second so after traveling 15 meters in five and a half seconds

the speed just happens to be also 5.5 meters per second that's their final speed

assuming constant acceleration that's very important assuming that they were always constantly

accelerating is that even possible well for rollerblader probably not but that's the assumption we have to make

of course every problem needs a final statement a conclusion therefore the final speed of the person is 5.5

meters per second two significant digits because of the 5500 milliseconds

which has two significant digits and the 15 meters all right at the very beginning of this

video you saw a stopwatch so now you're going to need a stopwatch if you don't have a stopwatch you could

always use the stopwatch feature on your personal electronic device

so here's the question here's the problem a real world problem determine the acceleration of a toy car

seen in the video as it slows down and comes to a stop so in a moment i'm going to show you

this toy car that will be moving forward it's a video i made myself and it's going to come to a stop

so again we have to assume constant acceleration in order to be able to use those formulas and that's a good

assumption in this situation our final speed is going to be zero that's one variable

because the car is going to come to a stop and so from the video we will determine

two things the displacement of the car and the time it takes to come

to a stop it's time for the video so here's the car and

it's going to stop somewhere out here the moment that this car passes this zero point imagine there's a line

here an imaginary line you're going to start your stopwatch so i'm only going to place video once you

have to be really quick here so have your stopwatch ready here we go remember

you're going to start your watch the moment it passes the zero and you're going to stop the watch when

the car comes to a complete stop so here we go are you ready car's going to stop momentarily

and there hopefully you stopped your stopwatch and hopefully you came up with a time

so remember our goal is to get two things from this video displacement and time

so the displacement it looks like the car is stopped around that grain of the wood and if we just

follow that grain of the wood back to the meter stick the displacement is around 0.52

meters i don't think i could be any more precise than that decimal

just because the car is a little bit too far away from the meter stick the time

the time i got was 13.45 seconds hopefully you got an answer similar to that

now the one thing you will have noticed is that the video was captured using the slow motion

feature on the personal electronic device most slow motion features currently on

the market slow down time by a factor of eight so what does that actually mean if on

the stop watch i got 13.45 seconds in real life in real life

the time if you're watching the event would have lasted 1.68 seconds and that makes sense

if you roll a car it doesn't roll for that long how did we get 1.68 we took our time of 13.45 and divided by

eight so whenever you record a video using the slow motion feature for most personal electronic devices

you have to divide the time by a factor of eight so now we have our three variables

we have our final speed we have our displacement and we have our time and our goal was

to always get the acceleration so once again there's our formulas and we're

hunting for the equation so let's see is it this equation here well it's got acceleration

it's got time it's got displacement but it has v1 in it it has initial speed no it's not that one let's look at this

one here does it have displacement yep does it have

the variable v2 yep does it have the time yes and does it have acceleration

yes that's it the other form of this don't work so this is the formula we're going to use

to solve for the acceleration so there's our formula delta d equals v2 delta t minus half a delta t squared

and we substitute 0.52 this is 0 because the final speed is 0 and this is our 1.68

we multiply this through 1.68 times 1.68 times half equals that number

zero subtract that number is simply that number and now we divide to solve for our

acceleration we don't subtract that's a common student error

instead we divide and our acceleration is negative 0.37 meters

per second per second what does that mean remember it's important to always try to

understand what acceleration means so it means every one second the car slows down by 0.37

meters per second and so our final concluding statement the acceleration of the car

assuming it is constant while slowing down is negative 0.37 meters per second

squared hope you enjoyed today's lesson have a great day bye