Different Cases of Position-time Graph

The position-time graph is one of the most important graphs in kinematics, which helps us determine a body’s motion. A position-time graph 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. 

Each point on the graph is a specific value of the variable at one particular instant in time. The points are connected with a line that shows the variable’s value at that instant in time.

What is the position-time graph?

A position-time graph displays the value of a stock at a particular instant in time on the Y-axis and the amount of time passed on the X-axis. The position of the stock on the Y-axis is measured from a starting point to the position at the time of the graph. 

The X-axis displays the amount of time that passed on the graph. The starting point on the Y-axis is often the first trade made by the investor when investing in the stock.

The graph on the X-Y plane

1. Take independent variables on X-axis 

2. Dependent variables should be taken on Y-axis

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

Position-time graph for a uniform motion

When all objects move in a uniform motion, they travel an equal distance in an equal time interval.

So, for the object moving in uniform motion, its position-time graph will be a straight line with respect to the time axis.

Here, we can calculate the object’s velocity by observing the object’s position as a function of time at any given point in time.

Main features of a position-time graph

We can use a position-time graph to help us understand the motion of an object. If an object moves at the same speed over a certain period, we expect a straight line on a position-time graph. 

However, if the object slows down or speeds up, we expect a curved line. This is because a curved line represents displacement, so we can see that the object’s speed has changed.

The position-time graph is a simple graph that displays the time taken to execute a function relative to the time taken for the same function execution earlier. The position-time graph is displayed on the call stack view for functions and is represented as a series of boxes stacked on top of each other. 

Each box represents the amount of time spent executing a particular code block relative to the previous block. The boxes are stacked so that they are executed in the program.

Speed-time graph(s-t graph)

A speed-time graph is a chart that displays the amount of time spent performing a task on a horizontal axis and the amount of work completed on a vertical axis. This graph shows how much time is spent working and how much work is completed on a specific task. The speed-time graph is most commonly used to measure output but can also compare results from one period to another.

When the moving object is accelerating, the slope of the graph will be positive, which represents an increasing speed.

When the moving object is decelerating, the slope of the graph will be negative, which shows the decreasing speed. 

Key points about the slope of the position-time graph

1. When calculating the instantaneous velocity of an object along a curve that changes over time, the slope of the tangent drawn at any point to the curve x-t gives you the instantaneous velocity.

2. If the slope is steeper, more will be the speed at that particular point.

3. The speed is given by the numeric value, which we get by the tangent slope.

4. We can calculate the direction of a particle, at a given time, based on the points where the slope of its position versus the time plot is zero.

5. Using the x-t graph, we can also know when the particle is moving at its maximum speed. The speed of a particle will be maximum at the point when the tangent, which is drawn to the x−t graph, is steepest.

Conclusion

A position-time graph 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 moves in a uniform motion, the objects travel an equal distance in equal time intervals. So for the object moving in a uniform motion, its position-time graph will be a straight line with the time axis. We can use a position-time graph to help us understand the motion of an object.