Distance Time Graph - Uniform Velocity

Dhristi JEE 2022-24

Distance Time Graph

The most popular and simpler method of presenting information about distance and time is through a line graph. The form of a line graph representing distance versus time is known as a Distance-time graph. Distance is usually placed along the y-axis and or the vertical axis, while time is generally put along the x-axis or horizontal axis. Hence, the distance-time graph is nothing but a simple line graph that indicates distance versus time findings on the map.


When we see an object moving with a uniform velocity, the graph's slope is always straight. In simpler words, the slope of a straight line of distance-time graph represents that an object moves with a uniform velocity. Distance time graph uniform velocity is a framework of a distance traveled by a body against time.


From this graph, we will know about the journey covered by a body along with its speed. For instance, in distance-time graph uniform velocity examples, if it is a straight horizontal line, the body is stationary with a zero speed. If the line is diagonal then moving with a constant speed and not a straight line, then the speed varies.


How to Draw a Uniform Velocity of Distance Time Graph?


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Choose two points on the line- (2, 20) and (5, 50)

Slope: \[\frac{\Delta y }{\Delta x }\], 

that gives us \[\left ( \frac{y_{2} - y_{1}}{x_{2} - x_{1} } \right )\]

Hence, the slope is 50-20/5-2 = 30/3 = 10

So, the ultimate velocity is 10m/s.


This particular calculation only works with uniform velocity. When it is not constant, the result will give you the average velocity of the two points.


How is a Velocity Time Graph Defined?

The graph that explains velocity against time is known as the Velocity-time graph. This explains how the velocity changes following time. The slope of a Distance time graph uniform velocity regulates acceleration.


In a distance-time graph, let us consider three objects as A, B, C, and all the three objects are in a horizontal position. Object A is considered as a flat horizontal line of a uniform velocity of the distance-time graph, which represents that the body is constantly moving. If the straight line consists of a slope, then it specifies that the body is changing its velocity at a continuous rate or it also means that the body has a constant acceleration.


Worksheet of Distance-Time Graph

Some of the solved mathematical problems of Distance time graph uniform velocity are represented here to help students get a good grip on the subject.


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Question 1: The above graph shows the journey of class 8th standard’s trip to the zoo. They halted to enjoy a picnic at the zoo. The following question’s answers are represented through the medium of graph

  • At what time the students stopped for a picnic?

  • For how long did they stop?

  • How far is the distance of the zoo from school?

  • At what time did the bus leave the school?

  • At what time did they arrive at the zoo?

  • How long had they traveled before stopping for a picnic?


Answers: 

  • 10.00 or 10 am

  • 30 minutes

  • 90 miles

  • 9.00 or 9 am

  • 11.30 or 11.30 am

  • 50 miles


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Question 2: Emma made a journey to her grandmother’s house and back. The graph presented above portrays the details of her journey.

  • For how long did Emma stay at her grandmother’s place?

  • How far was she from her house at 11.45?

  • At what time did she begin her journey?

  • What was the total distance traveled by Emma in total?

  • How far was Emma from home at 8 am?

  • At what time did she leave her grandmother’s house?


Answers: 

  • 1 hour 30 minutes

  • 7.5 miles

  • 7.30 am

  • 80 miles

  • 20 miles

  • 10.00 am


The graphical representations mentioned above show the calculation process of the uniform velocity of distance-time graph physics. Students must note that it is not possible to calculate smaller and larger values in the same graph. To learn more about different parameters of a graph, you can stay tuned with Vedantu’s online classes or students can download the official app of Vedantu to get easy access to PDFs, sample papers, and mock question papers.


If students register themselves on Vedantu’s online official website, they can view and solve different problems related to distance-time graph uniform velocity questions including their solved answers.


Particle Motion

As particles move along the x-axis, they move from the position of one coordinate to the position of the other. For example, from position x=0 to position x=2 (as shown below). In addition, a particle does not make a transition in the time interval t=0 to t=3 seconds.

 

Velocity Calculation

Let us first start with a particle at position x=0. Since the particle moves in only the x-direction, it is represented by the value x. Since the velocity at time t=0 is 0.0, its speed at any time t is simply the change in x: dx/dt.


For example, the particle at x=2 will move at a velocity of 2 units per second from x=2 to x=0. The velocity of this article would be 2 units per second if dx=2.0. The velocity can be represented in one of two ways:

  1. dx=2.0 units, dt=0.01 seconds

  2. dx=-2.0 units, dt=-0.01 seconds


This means that there are two values for velocity in one second. The first particle has a velocity of 2.0 units, and the second particle has a velocity of -2.0 units.


In the graph below, we see the particle at the bottom of the graph. The graph shows how long it takes the particle to reach different positions. Each timestamp represents 1/10th of a second.


For example, the particle takes 0.1 seconds to reach x=1.8 and t=0.1 seconds. The particle takes 0.8 seconds to reach x=-1.8 and t=0.8 seconds. These times are represented in the graph above.


The difference between a particle and a person traveling at a constant speed in a straight line can be represented as follows. Imagine that you have two balls, one being at a constant speed and the other being a ball at rest. When the two balls meet, the one at rest has traveled half as far as the one at a constant speed. A constant velocity represents a particle that is moving without change.


The Particle changes its Direction of Motion

The particle continues to travel at the same velocity in the same direction. However, the direction of motion does change over time.


In some situations, such as a comet, the particle travels in one direction for a short period of time before reversing direction. This is represented by changing the direction of the velocity. In physics, the change in direction is called angular velocity. It is represented as d/dt. Angular velocity is given in units of radians per second.


This graph shows the particle changing direction. The two points with red X's represent the two velocity vectors as measured at two different time points. The particle was traveling on a straight line at a constant speed.


The Velocity is Perpendicular to the Direction of Motion

A velocity vector can have both a direction and magnitude. The velocity of a particle can be in any direction in space, and the speed of the particle can be either positive or negative.


In a frame of reference, the direction of motion can be represented as a right angle. The velocity is perpendicular to the direction of motion. The equation V=d/dt can be used to represent the velocity in this type of situation.

 

Velocity Changes in Opposite Directions

The particle travels in a straight line for a period of time. Then, it travels in the opposite direction for a period of time.


For a stationary object, the distance covered is the same in both directions. Since the velocity of the object is a vector, its magnitude is also the same, and therefore the distance travelled is the same.


If an object travels in a straight line for a period of time, then the distance it travels is the same as the time it takes to travel this distance. If this distance is the same in both directions, then the object is at a rest. This can also be described as the object traveling in a straight line with constant velocity, where the velocity is zero.


To find the velocity of an object in an equation, the change in distance can be divided by the time taken to travel this distance. If the velocity of a particle changes, there are several cases that can occur:


Case 1: The change in direction and magnitude is 90 degrees.


This is called the same velocity in opposite directions. The particle travels in a straight line for a period of time. Then, it travels in the opposite direction for a period of time. A diagram for a particle travelling in a straight line with constant velocity for a period of time, then travelling in the opposite direction for a period of time.


When the velocity of a particle changes, the distance covered in the opposite direction is smaller than the distance covered in the original direction. This is due to the fact that the particle is moving in the opposite direction for a smaller amount of time.


When the distance covered in the opposite direction is less than that of the original direction, the particle is speeding up. The equation for a particle that is speeding up can be found by dividing the change in the distance by the time taken to travel the same distance. The amount of distance covered by the particle that is speeding up can be found by multiplying this ratio by the original distance

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FAQs (Frequently Asked Questions)

1. Is Graph Theory Complicated?

When compared to the higher-level math classes, a theory of graph is comparatively easy. Moreover, high-standard maths will require more time and effort. However, distance-time graph uniform velocity includes lots of proofs. So if students are not very acquainted with explanations, then they will find graph theory classes complicated. The topics that are generally taught in the introductory graph theory class are relatively easy. However, the proofs in algebra and real analysis are quite difficult to understand. To make graph theory easier, students must thoroughly understand the chapters instead of jumping straight to the problem.

2. There are 9 Line Segments Drawn on a Plane. Is it Possible to Intersect Each Line Segment in Exactly 3 Others?

Initially, the problem seems to be quite difficult to understand. The problem can be solved by using a graph. If students consider line segments as edges of a map, it is impossible to reach any solution. Hence, they need to consider such a graph where each line segment represents a vertex. Now, the two vertices of the graphs are associated with each other if the parallel lines intersect.

The graph has 9 vertices. The degree of each vertex is 3

The summation of degrees of all the vertices = 2x no. of edges in the graph.

However, a sum of degrees of all vertices in the above mathematical problem is 9x3=27, i.e. an odd number. Hence, such an arrangement is not possible.

3. What is the Importance of Distance-time Graphs?

To understand distance-time graph uniform velocity, students need to study the motion of bodies. If they note a body’s movement's distance and time and place it on a rectangular graph, they will obtain a distance parallel to its motion. It also helps them to understand whether an object is moving at a constant or variable speed. With this particular graph, students can quickly determine the time taken to cover a specific distance in a short time. This graph shows a motion’s uniformity or non-uniformity and also whether it is accelerated or retarded.


Hence, information about motion and velocity can be represented in many ways. With tabular representation, it gets simpler for students to figure out complicated mathematical problems easily.

4. How to memorize physics concepts for a long time?

Physics is a natural science that is all about the study of matter around us, its behavior, and its application. It is basic physical science.  Students can make mind maps and write down formulae for better understanding and it also helps in retaining the concepts for a longer period of time. At Vedantu, we provide revision notes and keywords which would help students in saving time in preparing the notes and assist them in chapter-wise revision. 

5. How to manage time while writing a physics exam?

Many students say that though they went prepared to give their physics exam, due to the lengthy and tricky questions, it became difficult. To avoid such an experience students are recommended to practice writing faster and memorizing the keywords. Also working out objective-type questions beforehand saves time in analyzing and answering them. Lastly, students are advised to divide their time into sections namely A, B, C, and D and attempt all the questions without fail.

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