# Relationship between average velocity and slope

### Average Velocity and Angle of Inclination of a Slope | Physics Forums The slope of a position graph represents the velocity of the object. . The average slope between two points in time will give you the average velocity between. 1-D Kinematics - Lesson 4 - Describing Motion with Velocity vs. Observe the relationship between the slope of the line during each four-second interval and. What is the relationship between a ball rolling down a slope (ramp) and its average velocity. I know we are supposed to use: v^2 = ut + at/2 and. 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.

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. Negative slope does not automatically mean driving backward, or walking left, or falling down. The choice of signs is always arbitrary. About all we can say in general, is that when the slope is negative, the object is traveling in the negative direction. On a displacement-time graph… positive slope implies motion in the positive direction.

There is something about a line graph that makes people think they're looking at the path of an object.

### How is average velocity related to the secant line? | Socratic

Don't think like this. Don't look at these graphs and think of them as a picture of a moving object. Instead, think of them as the record of an object's velocity. If we make a graph of position vs time and our object is moving at a constant velocity, the graph will form a straight line. We generally put position on the y-axis, and time on the x-axis.

We call this a linear graph. The slope of this line will be the average velocity of our object. If the graph is flat or horizontal, then the object is not moving, the slope is zero, and the velocity is zero. It is important that when you have a graph, there is a title, axes labels, and units. The faster the object goes, the greater the slope of the graph. In the following graph, you can see an object which is incrementally speeding up. Slow, fast, and faster. This is particularly useful for when there is a lot of noise in our data.

In middle school, you may have learned to draw a best fit line by hand using a ruler. Computers calculate the best fit line using an algorithm called the Least Squares Fit. The computer calculates the error at every point, and tries to minimize the square of that error. We can calculate the slope of the following graph. From middle school math, you may remember that you find the slope by taking the rise over the run.

## Graphs of Motion

Whenever you have a graph, you can always analyze the graph. It is not enough to merely say the graph goes up! The slope of the graph provides you with information, such as the velocity. For a position vs. We should point out that if the slope is positive, then the velocity is positive.