### What are acceleration vs. time graphs? (article) | Khan Academy

Constant acceleration motion can be characterized by motion equations and by motion graphs. The graphs of distance, velocity and acceleration as functions of. Because acceleration is velocity in m/s divided by time in s, we can derive a graph of The acceleration graph shows that the object was increasing at a positive constant Calculations with constant acceleration can be done in relation to. Let's begin by graphing some examples of motion at a constant velocity. . Compare the velocity-time equation for constant acceleration with the classic.

When the two points coincide, the line is tangent to the curve. This limit process is represented in the animation to the right.

## Constant Acceleration Motion

Seven tangents were added to our generic displacement-time graph in the animation shown above. Note that the slope is zero twice — once at the top of the bump at 3.

The slope of a horizontal line is zero, meaning that the object was motionless at those times. Since the graph is not flat, the object was only at rest for an instant before it began moving again. Although its position was not changing at that time, its velocity was.

## Graphs of Motion

This is a notion that many people have difficulty with. It is possible to be accelerating and yet not be moving but only for an instant, of course. Some interpret this as motion in reverse, but is this generally the case?

Well, this is an abstract example. It's not accompanied by any text. Graphs contain a lot of information, but without a title or other form of description they have no meaning.

### Graphs of Motion – The Physics Hypertextbook

What does this graph represent? A mote of dust?

About all we can say is that this object was moving at first, slowed to a stop, reversed direction, stopped again, and then resumed moving in the direction it started with whatever direction that was. Because we haven't been given any values on the vertical axis of the displacement-time graph, we cannot figure out what the exact gradients are and hence what the values of the velocity are. In this type of question it is just important to show whether velocities are positive or negative, increasing, decreasing or constant.

Once we have the velocity-time graph its much easier to get the acceleration-time graph as we know that the gradient of a velocity-time graph is the just the acceleration. For the first 2 seconds the velocity-time graph is horizontal at zero, thus it has a gradient of zero and there is no acceleration during this time.

This makes sense because we know from the displacement time graph that the object is stationary during this time, so it can't be accelerating. For the next 2 seconds the velocity-time graph has a positive gradient. This gradient is not changing i. For the final 2 seconds the object is traveling with a constant velocity.

### FHSST Physics/Rectilinear Motion/Graphs - Wikibooks, open books for an open world

During this time the gradient of the velocity-time graph is once again zero, and thus the object is not accelerating.

The acceleration-time graph looks like this: A brief description of the motion of the object could read something like this: Worked Example 25 Calculating distance from a velocity-time graph[ edit ] Question: The velocity-time graph of a car is plotted below. Calculate the displacement of the car has after 15 seconds.

We are asked to calculate the displacement of the car.