In this simulation, two objects move. The blue object moves with constant velocity, while the red object moves with constant acceleration. In physics, we often model various motions as either constant-velocity motion or constant-acceleration motion, so this simulation gives you a way to contrast these two motions.
Graphs of the position versus time, as well as the velocity versus time, are shown for both motions. Such graphs can provide a lot of information, including:
- the slope of the position versus time graph at a particular instant is the velocity at that instant. Because the blue object has a constant velocity, the position versus time graph for the blue object has a constant slope. On the other hand, the red object has a constant acceleration - if this acceleration is not zero, then the red object has a constantlychanging velocity, so the red object's position versus time graph has a steadily changing slope.
- the area under the curve of the velocity versus time graph is the displacement (the change in position). For constant-velocity motion, this area is rectangular in shape, so the area is very easy to calculate. For constant-acceleration motion, the area is triangular, so that's fairly easy to work out, too.
Equations of motion
For motion with constant acceleration, the equation giving the velocity as a function of time is:
v = vi + at
and the equation giving the position as a function of time is:
x = xi + vi t + (1/2)at2
With no acceleration, that equation reduces to the constant-velocity form:
x = xi + vi t