Slope Denotes in the Position-Time Graph

A position-time graph is a plot of positions versus time. It shows the relation of positions to time in space or time but may not show the trajectory of those positions as they move. In physics, position-time graphs describe the velocity of a particle in time and space. The graph depicted above shows the velocity of a particle as a function of position and time. These graphs are used to describe the motion of an object in space and time that are a function of position and time in space. They describe the motion of a particle in a space but can be applied to any motion.

What is the Position-Time Graph?

A position-time graph displays the value of a stock at a particular instance in time on the x-axis and the amount of time that passed on the y-axis. The position of the stock on the x-axis is measured from a starting point to the position at the time of the graph. The y-axis is used to display the amount of time that passed on the graph. The starting point on the x-axis is often the first trade made by the investor when investing in the stock.

The Graph on the X-Y Plane

The graph on the X-Y plane has the following characteristics:

1. It must take independent variables on the x-axis.

2. Dependent variables should be taken on the y-axis.

3. There must be mathematical calculation; the dependent variable is too dependent on the independent variable.

The Slope

The slope of a curve at any point is defined as the tangent (tanθ) of the angle made by the tangent at the given point with the x-axis. It is denoted by m. If we take two points, such as (x1, y1) and (x2, y2), on the curve, then the slope is written as:

m(slope) = (y₂-y₁)/ x₂-x₁

To find the slope of a graph at a single point, take the differentiation of the function and find its value at that given point.

The slope of an x-t time graph leads us to the velocity, and the slope of a velocity-time graph leads us to the acceleration.

In this figure, the slope of a position-time graph can be written as:

Slope = ⅆx/ⅆt, which is the velocity of the particle.

The same can be defined for the acceleration of the velocity-time graph.

Calculating Velocity from the Position-Time Graph

An object’s average velocity can be calculated from the position-time graph with a constant slope. The average velocity is given by the total change in position divided by the total change in time.

V = Δd/Δt 

In the graph above, we can find the velocity because of the presence of a constant slope, indicating constant or positive velocity and no acceleration. Here, we can directly calculate the slope by applying the rules of trigonometry. The value obtained will give us the value of velocity. We will see a case where the calculation of velocity is not directly possible in the next section.

Uses of Position-Time Graphs

Position-time graphs are useful in the following ways:

1. They help in detecting the motion of an object in different instances. 

2. It helps in the calculation of average velocity.

3. A position-time graph can be used to analyse of a stock price, for example, or for forecasting future market activity.

4. It can be used to find relationships between two data sets (for example, time and years of education).

5. We can visualise the path of the object using these graphs and calculate the maximum velocity of the particle by obtaining the value of the steepest point of the slope.

Conclusion

A position-time graph is a graph that shows the changes in the values of a variable over time. Time is usually represented on the vertical axis and values on the horizontal axis of a position-time graph. When an object is moving in a uniform motion, the objects travel an equal distance in equal intervals of time. So for the object moving in uniform motion, its position-time graph will be a straight line with respect to the time axis. We can use a position-time graph to help us understand the motion of an object.