Position Time Graph

One of the most elementary forms of graphs in kinematics is the Position-time graph, which helps us to define the motion of a body. In these graphs, the position of the object is represented by the vertical axis, the time elapsed is represented by the horizontal axis, and the dependent variable, that is position, depends on the independent variable, that is time. In this way, the graph expresses to us where the particle can be found after some time.

These graphs help us visualise the path of objects. By studying a position-time graph for an object, we can analyse the path and position of an object precisely.

Table of Contents

• About the Position Time Graph
• Description of Position Time graph for uniform motion
• Explanation of Position Time graph for uniformly accelerated motion
• Important points about the slope of Position Time graph
• Position Time vs Distance Time vs Displacement Time graph
• Frequently Asked Questions – FAQs

What is the Position Time Graph?

The graph on which the instantaneous position x of a particle is plotted on the y-axis and the time t on the x-axis is known as the Position-Time graph.

Since this article is an explanation of the position-time graph, before digging deep into the details of the topic let us first understand how to draw these graphs.

To draw graphs in x-y- plane

• Always take an independent variable on the x-axis.
• Dependent variables should be plotted on the y-axis.
• Through some mathematical function the dependent variable is dependent on the independent variable.

In the case of the Kinematic equation for uniformly accelerated motion, position is a dependent variable and time will be our fundamental independent variable. Also, the other dependent variables will be displacement, velocity, and acceleration.

Description of Position Time graph for uniform motion

When an object is in uniform motion it travels an equal distance in equal intervals of time.

Therefore, in uniform rectilinear motion the Position-time graph for an object is a straight line inclined to the time axis.

Here, the velocity of the object can be calculated using Position vs time graph slope.

To find the slope of x-t graph refer to the figure given below

Here you can see that at time t = 0, the object is at x_o, at time t = t₁ the object is at X₁ and at time t = t₂ the object is at x₂.

Here theta is the angle which the x-t plot makes with the x-axis.

Position vs time graph slope = slope of line AB

=tanθ=QR/PR = x₂–x₁/ t₂–t₁

=Displacement/time= velocity(v)

Explanation of Position Time graph for uniformly accelerated motion

For uniformly accelerated motion along a straight line the Position Time relation will be given as,

x = x_o + u_ot + ½at²

Here, x depends on t² which shows that it is a quadratic equation of function t, therefore, for uniform accelerated motion the position-time graph is a parabola.

As established earlier, the slope of the x-t graph signifies the velocity of an object. Here, in the case of uniform accelerated motion, the instantaneous velocity is represented by the slope of the position-time graph.

Slope of the x-t graph at time t=0 signifies the initial velocity v_o of the object.

Let us compute the slope of the x-t graph for uniform accelerated motion.

The slope of the x-t graph =

Important points about the slope of Position Time graph

• The instantaneous velocity can be calculated using the slope of the tangent drawn at any point to the x-t curve.
• Steeper the slope at any point, more is the speed at that point.
• The numerical value of the slope of the tangent gives the speed.
• The direction of the change in motion of a particle at a particular instant can be computed using the points where the slope of x−t plot is zero.
• Using the x-t plot, we can also compute the instant when the particle is moving with the maximum speed. The speed would be maximum at the instant where the tangent is drawn to the x−t plot is steepest.

Motion Graphs | Velocity-Time Graph and Displacement-Time Graph :

Position Time vs Distance Time vs Displacement Time Graph

There is no difference between the position-time graph (x-t) and the displacement-time graph; both these graphs talk about the precise change in position of a body.

So, basically it talks about the shortest distance between initial and final position, w.r.t time, irrespective of the actual path used. A distance-time graph represents the distance covered, that is the exact length of the actual path followed from the initial point to the final point, with respect to time. A distance-time graph does not care about the direction in which the objects are travelling.

Stay tuned to BYJU’S for more such interesting and informative articles. Also, register to “BYJU’S – The Learning App” for loads of interactive, engaging Physics-related videos and unlimited academic assistance.

Related Articles

• Motion in Physics
• Newton’s Laws of Motion
• Instantaneous Speed and Instantaneous Velocity