in this video we focus on an example of a car speeding up from rest we learn to plot
the motion on a velocity time graph and then we quantify how fast the car is speeding up
and that's called the acceleration finally we plot the motion on an acceleration time graph
and we learn to interpret the signed area bounded by that graph so in our example we're told that a
car speeds up from rests starting from the origin and gets to 100 miles per hour in 10 seconds
the motion is always in a straight line and the car speeds up at a constant rate so in part a we
want to plot the motion of the car on a velocity time graph and a point on this velocity time graph
of course has two coordinates the first one is what time is it in seconds and then the second
coordinate is what's the velocity in miles per hour so if i look at a time of t equals zero
i'm told that the car was at rest at that moment in time and i get my first point on the velocity
time graph it's just the origin because the car was at rest when we started the clock the only
other point we know is that when t is equal to 10 seconds the velocity is going to be positive 100
miles per hour and the grid spaces in the vertical direction we're going to take those to be 10 miles
an hour each there's the plus 50 miles per hour for reference and there's 100 miles per hour
so again we know the car is moving at plus 100 miles per hour when t is equal to 10 seconds
that's our second ordered pair that we know on the graph finally we're told that the car
speeds up at a constant rate and this means we can connect those two points with a straight
line the car is speeding up uniformly in part b we're asked to compute the slope of this graph
and then comment on the physical meaning of that slope so we look at the rise and the run and the
rise here the change in the vertical coordinate is plus 100 miles per hour and the run that's
the change in the horizontal coordinate is plus 10 seconds so i get the slope and i'm careful
to keep the units on this and rather than trying to smash together the time units here
i think it's most intuitive to just keep it as 10 miles per hour per second and so all this means
is that as the car is speeding up it's speeding up by 10 miles per hour every time one second goes by
and certainly we can see this in the graph it starts from rest and then i go over one
second and up 10 miles per hour and after one second it's moving 10 miles per hour
after another second it's moving 20 miles per hour after another second 30 miles per hour and
so on so every time a second goes by this thing speeds up by 10 miles per hour and that's what 10
miles per hour per second means and the name for a rate of change in velocity is the acceleration and
we get our first major fact of this video and this lives in a box because it's so important
the slope between two points on a velocity time graph gives you the average acceleration next
we're asked to plot an acceleration time graph for the same car and we're using
those same units of acceleration of miles per hour per second for the car just because those
were very natural units for the context and so for every moment in time we want to plot
the acceleration but that acceleration was always the same number it was 10 miles per
hour per second so with the value of acceleration always being the same no matter what time it is
this is a horizontal graph and it will extend all the way to when t is 10 seconds and there's the
plot of our acceleration as a function of time and then in part b we're asked to compute the
area bounded by this graph and then comment on the physical meaning of that area so the area bounded
by this graph is just the area of this square but we need to be careful to keep the units here and
the height of the square is 10 miles per hour per second and the width of the square is 10 seconds
when i compute the area the seconds cancel and this gives me 100 miles per hour
and that's positive because this acceleration is above the t axis it's a positive acceleration
so what did that give us physically that was the change in velocity for the car
as it was accelerating it went from 0 to 110 seconds and this gives us our second major fact
of the video and we'll give this guy a box as well the area bounded by an acceleration time
graph gives you the change in the velocity if you enjoyed this video or at least found it
useful check out another one by clicking one of the links on the left or click the zaxlab logo
on the right to explore dozens of physics and math playlists as always you can leave your questions
comments and requests in the comments section below and i'll get back to you within 24 hours
thanks for watching zach's lab and best of luck on your math and physics journey