Make a Position-time graph

A position-time graph is a plot of positions versus time, showing 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  shows the velocity of a particle as a function of position and time. Position-time 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 are used to describe the motion of a particle in a space, but they can be applied to any motion.

How to make a position-time graph?

Step 1: Take the y-axis as a position relative to the starting point since the position is a dependent variable, and dependent variables are taken on the y-axis.

Step 2: Take the x-axis as time since time is an independent variable, and independent variables are always taken on the x-axis.

Step 3: Mark the distance travelled at different instances of time. This will give you a straight line, which will either have a zero slope or a positive slope.

When a body travels equal distances in equal intervals of time by keeping its velocity constant, it is called uniform rectilinear motion. Since this graph represents the same conditions and an inclined slope, this graph represents a uniform rectilinear motion.

Features of a position-time graph:

1. This graph will tell the distance travelled by a body starting from its initial point.

2. The straight line obtained in the graph after marking all the points gives the velocity of the object.

3. If the slope is positive, it means its velocity is increasing. More the slope, the greater the velocity.

4. A horizontal straight line in the graph indicates a constant velocity which means that the position of the object is not changing.

5. Position-time graph tells you about the motion of an object at different instances.

Calculation of velocity from position-time graph:

The average velocity of an object 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 the detection of 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 for an analysis of a stock price, for example, or for forecasting future market activity, etc.

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.

Curvature in a position-time graph:

The curvature in the position-time graph represents that the velocity is constantly increasing or decreasing at regular intervals of time. The motion is either acceleration or deceleration and is called uniformly accelerated motion. Hence, the slope of the curve is constantly changing and shows a parabola. This is because, for a uniformly accelerated motion, the distance is a function of the square of time, and the shape of the graph is a parabola for squared functions.

In short, if the graph is an upside parabola, the motion has negative acceleration, whereas if the graph has a downward parabola, the acceleration is positive. Such curves or graphs represent a uniformly accelerated motion.

This graph is also a position-time graph but is not forming a straight line, hence indicating that an object is suffering deceleration(due to upward parabola in this case) and the velocity is not constant. In this case, we can not directly calculate the average velocity but can only find instantaneous velocity by methods of integration and differentiation. 

Conclusion

Position-time graphs are used to describe the motion of an object in space and time that are a function of position and time in space. The average velocity of an object can be calculated from the position-time graph with a constant slope. The curvature in the position-time graph represents that the velocity is constantly increasing or decreasing at regular intervals of time. The motion is either acceleration or deceleration and is called uniformly accelerated motion. When a body travels equal distances in equal intervals of time by keeping its velocity constant, it is called uniform rectilinear motion.