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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 Distance-time graph. Distance is usually placed along the y-axis and or the vertical axis, while the 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 travelled 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.

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

Slope: Δy/Δx, that gives us ( y2-y1 /x2-x1)

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.

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. The object A is considered as a flat horizontal line of a uniform velocity of 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.

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 from the school?

At what time did they arrive at the zoo?

How long had they travelled 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 travelled by Emma in total?

How far was Emma from home at 8 am?

At what time she left 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 shows the calculation process of 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 PDF's, 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.

FAQ (Frequently Asked Questions)

1. Is Graph Theory Complicated?

Ans: 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?

Ans: 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. 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?

Ans: 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.