Converting Velocity Time Graphs to Acceleration Time Graphs

good morning today our goal is to learn about converting a velocity time

graph to an acceleration time graph and so here's a velocity time graph and the previous video i showed you how

to convert this velocity time graph into a position time graph however today we're going to take this

velocity time graph and ultimately convert it into this what we're looking at

is an acceleration time graph so that's our goal today to learn how to take that velocity time graph

and create a graph that looks like this and so for starters we're going to describe this graph

so for the first section from 0 to 4 seconds it's constant velocity the velocity is

not changing 4 meters per second north for section b because a line is drawn this represents

constant acceleration and in fact the car in this case

is slowing down moving north and finally for section c from 7 to 10 seconds the car is taught

so how do we go from a velocity time graph to an acceleration time graph what do we have to do to get there

for starters we need to calculate the acceleration to do that we need to calculate the

slope of each section of the graph we need to calculate the slope

for each line slope is rise over run and looking at the first section there

is no rise the rise is zero the run is four seconds and so

for section a from zero to four seconds the acceleration is exactly zero how do we plot this

on a graph well this is how we plot an acceleration of zero

it's just the line across the x-axis notice that the line ended at four seconds why was that

well it ends at four seconds because section a ends at four seconds in other words the

acceleration changes at the four second point that's why we stop drawing the line at

four seconds all right now that we've plotted the acceleration for the first part of the

graph from 0 to 4 seconds what about the next section of the graph section b

once again to calculate acceleration we need to find slope slope is rise over run

so we've drawn there the rise and the run the rise is negative four meters per

second the velocity is decreasing it's not increasing so that's why it's negative

the run is three seconds how do we know it's three seconds well this line starts at four

and ends at seven seconds the time that's elapsed is three seconds and so we do our math we substitute our

numbers into the equation rise over run negative four over three

and we end up with this answer negative four thirds or negative one point three three meters per second

per second so how do we plot that in an acceleration time graph well we draw a line that line is drawn at

negative 1.333 meters per second per second or negative four thirds

meters per second per second that line starts at four seconds and ends at seven seconds because

section b started at four seconds and ended at seven seconds

what about section c the rise is zero the run is three seconds and we end up with an

acceleration of zero and that's how we plot the last part of the graph it starts at 7

seconds and ends at 10 seconds and so the question is this if we look at the graph and specifically we look at

the four second point the car seems to instantaneously accelerate from a value

of zero to a value of negative four over three meters per second per second

is this even possible is the transition at four seconds realistic similarly at seven seconds

is the transition realistic the answer is no in real life you would never get that instantaneous

change in acceleration it's impossible for a car and so the reality is there would be a

smooth transition and i've shown you that smooth transition at the four second point and at the

seven second point however for simplicity we're going to ignore that there's a smooth transition

all right so here's the task i'd like you to complete here's the velocity of a car for 15

seconds this time we have five different sections of acceleration

i'd like you to calculate the slope for each section and then try to create an acceleration

time graph ultimately if you really want to understand physics

you have to practice these skills here is the answer you should get

once you complete all your work so give it a try i hope you've enjoyed today's lesson

have a great day bye