Position versus time graphs

Although understanding the numerical aspects of physics with equations and derivations may be tedious, doing it with the aid of graphs can be both engaging and straightforward, making it easier to comprehend what the solution is describing. Graphs play an essential part in Physics since they are used in almost all ideas.

Position versus time graphs

There is a common perception among individuals that graphs are as frightening as going to the dentist. There is an overwhelming desire to get the experience over with as fast as possible. On the other hand, Position graphs may be aesthetically pleasing. They show the x-axis is helpful for graphically conveying a large quantity of information about an object’s motion in a minimal amount of space.

On a position graph, the vertical axis shows the position of the item. Consider the following example, if you read the value of the graph at a specific moment, you will receive the distance between the object and the reader.

On a position graph, what does the slope represent?

Position graphs have a slope that reflects the velocity of an object. As a result, the slope value at a given moment corresponds to the item’s velocity at that point.

The slope of this position graph is defined as slope= rise/run=  x₂-x₁t₂-t₁

v = ΔxΔt = x₂-x₁t₂-t₁

The definition of slope is the same as the definition of velocity, which is as follows: the slope of a position graph must be the same as the velocity.

When the slope of a position graph changes, that means velocity changes. If the slope of the curve is oriented upward, the slope of the curve between the intervals is positive. This indicates that the velocity is positive.

If the direction of the slope is downwards, the slope of the curve is negative. This indicates that the object’s velocity is negative.

The Position-Time Graph

The position-time graph depicts the movement of an item throughout a certain period. A standard time graph shows the x-axis in seconds, and the y-axis represents the item’s position in metres. In this case, the slope of the position-time graph provides valuable information regarding the object’s velocity.

The slope of the Position-Time Graph

The slope of a position-time graph indicates the sort of velocity that an item experiences while in motion. A position-time graph with a constant slope shows that the velocity is constant. An increasing or decreasing slope on a position-time graph indicates the velocity changes. The sign of the velocity is shown by the direction of the slope of the position-time graph. Suppose the slope is downhill and runs from left to right. In this case, the velocity is negative.

The Velocity-Time Graph

It is possible to determine the speed at which an item is travelling at a particular moment by looking at its velocity-time graph and whether the object is slowing down or speeding up. Temporal data is often represented on the x-axis in seconds, whereas velocities are typically plotted on the y-axis in metres per second. An object travelling at a constant speed has a velocity-time graph that is a straight line. Sloping, linear velocity graphs are produced by objects moving at different speeds.

The slope of the Velocity-Time Graph

It is possible to determine the acceleration of an item by examining the slope of a velocity-time graph. If the slope of the velocity-time graph is a horizontal line, then the acceleration is equal to zero. This indicates that the item is either at rest or is travelling at a constant speed, without increasing or decreasing its speed as it approaches. If the slope is positive, the acceleration is rising in magnitude. If the slope is negative, this indicates that the rate of acceleration is declining.

Developing the Equations of Motion is a difficult task.

Following the definition, acceleration is defined as “the rate at which a given velocity changes with respect to time, “and in the context of a particular velocity-time graph, it may be expressed as “the slope of the graph.”

a= dvdt = slope of the graph results from deriving the equations of motion.

⇒ v = u+at

The displacement of the particle may be calculated from the area beneath the velocity-time graph.

Now, using the first equation of motion, we may say

(v–u) = at

From the equation of motion, displacement can be given as

s = ut + 12at2

If we insert the value of ‘t’ from the first equation of motion into the provided equation, we get the following result

We obtain t=(v–u)/a as a result.

⇒ s = u(v-u)a+12(v-u)2a 

When we solve the equation mentioned above, we get the following result:

⇒ v2 = u2 + 2as

Summary

During this lesson, we studied the laws of motion. We spoke about the position-time and velocity-time graphs in various circumstances and scenarios. The equations of motion for constant acceleration were also obtained using the velocity-time graph. We discovered that one of the limitations of these equations of motion is that the acceleration must be constant throughout the equation.