Don’t mind doing this because I hate to see former students struggle, and besides
I can always make these available for my daughter and other current students.
(1)Let’s start with the easiest graph...
distance
time
Always make sure you’re aware of the scales on the axes.
So here over the course of time, the distance is not changing. The slope is zero,
which means the car isn’t moving. Its velocity is zero. In other words, the slope of
a distance-time graph is velocity.
(2)
Now here is another situation
distance
time
This is a direct variation, straight line with a constant velocity. So the now the car
is moving , covering the same amount of additional distance every second. Get
the slope, and you have found the velocity.
(3) If we want to represent the same above situation on a velocity-time graph,
the above would look like this:
velocity
The velocity is not changing over
the course of time; in other words
it’s not accelerating.
time
The slope on a velocity –time graph is acceleration. Since the velocity is constant,
then there’s no acceleration. Makes sense, since the slope is zero on the above v-t
graph.
(4) Accelerating situation on the original distance-time graph would be a
parabola. This is consistent with the formula d= vt + 0.5at2
The slope keeps changing an keeps
getting steeper because the slope if
you recall on a d-t graph is velocity.
So if it’s accelerating, obviously the
velocity increases every split second.
(5) But if it’s constant acceleration,
the velocity increases at the same
rate, so if you turn this situation into
a v-t graph like we did earlier for
situation 2, now we will get:
Are you still with me. Is physics back from hell? So what does slope on this graph
represent? Yes.
Acceleration.
Acceleration is the
slope on a velocity
versus time graph.
(6) So if we plot
acceleration
versus time for the
above situation we
get
acceleration
time
So the previous three graphs are three representations of the same thing.
Changing the nature of the y axis gives three different pictures, but they all
symbolize a car accelerating .