What are the characteristics of the distance time graph for an object moving at a uniform speed class 9?

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Question 1 What is the nature of graph for a uniform speed?

Question 2 Name the quantity which is measured by the area occupied under the velocity-time graph?

Question 3 What does the slope of speed-time graph indicate?

Question 4 What can you say about the motion of a body if its displacement-time graph is a straight line?

Question 5 What can you say about the motion of a body if its velocity-time graph is a straight line?

Question 6 Name the quantity, the slope of whose graph give Speed?

Distance – Time graphs

(1) Uniform Speed

Straight line graph between distance and time tells us that body is moving with uniform speed. Slope of distance time graph indicates speed.

(2) Non-Uniform speed

The distance time graph for a non-uniform motion is a curved line (parabola). If a body moves with a non-uniform speed then its motion is said to be accelerated. It also represents distance time graph with accelerated motion.

Speed – Time or velocity – Time Graphs

(1) Speed-time graph when speed remains constant

(a) Speed time graph for a body moving with constant speed(no acceleration) is a straight line parallel to time axis. We can find the distance travelled by a body in a given time from speed-time graph.

Speed = Distance travelled / Time taken

OC x BC = Distance travelled
OC x OA = Time taken
Distance travelled = Area of rectangle OABC

The velocity time graph of an object moving with constant velocity is a straight line parallel to time axis.

(2) Speed-time graph when speed changes at uniform rate (uniform acceleration)

(1) When a body moves with uniform acceleration,its speed changes by equal amount in equal intervals of time.

Speed time graph for a uniformly changing speed will be a straight line. 
The value of acceleration from speed time graph of moving body can be calculated as:

a = Change in speed or velocity / Time taken

a = PQ/OQ

In a speed time graph the acceleration is given by slope of the graph.
The distance travelled by a moving body in a given time can be calculated from speed time graph.

Distance travelled = Area of triangle POQ
= 1/2 x OQ x OP

In a speed time graph of a body a straight line sloping downwards indicates retardation.

Speed time graph when the initial speed of the body is not zero.

The distance travelled by the body in this case is equal to the area of trapezium OBCA.

                      Area of Trapezium =  (Sum of parallel sides x Height) / 2
 Distance Travelled =  (OB x AC) x OA)/2

(3) Speed – Time graph when speed changes at a non-uniform rate (Non-uniform acceleration)

1. Curved line
2. Straight line
3. Line parallel to X axis 
4. Line parallel to Y axis

Answer: (2)

Distance-Time Graph for Uniform Motion

A body is said to be in uniform motion when the body covers the equal distance in equal time intervals. Let’s consider a time interval of 1 second, If a body covers 10 meters in the first 1-second then it should cover 10 meters in every second from there on, this will indicate that the body is in uniform motion. Let’s draw a graph for uniform motion.

As in uniform motion, the distance time graph would be a straight line, because the equal distance is covered in equal units of time.

Distance-Time Graph for Non-uniform Motion

Non-uniform motion is defined as the motion of an object in which the object travels with varied speed and it does not cover the same distance in equal time intervals, irrespective of the time interval duration.

The distance-time graph for non-uniform motion is not a straight line since speed is variable, it can be a curve or a zigzag line.

Watch the video for understanding motion graph

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A distance-time graph shows how far an object has travelled in a given time.  It is a simple line graph that denotes distance versus time findings on the graph.

1. Distance is plotted on the Y-axis.
2. Time is plotted on the X-axis.

Note: Curved lines on a distance-time graph indicate that the speed is changing.

You may also want to check out these topics given below!

• Graphs
• Velocity-Time Graph
• Linear Graph

Importance of Distance-Time Graph

We deal with the distance-time graph while studying the motion of bodies. If we record distance and time for the motion of a body and plot the same data on a rectangular graph, we will obtain a distance-time graph corresponding to the motion of that body.

Example:

For better understanding, let us consider an example of uniform motion. A bus driver drives at a constant speed which is indicated by the speedometer and the driver measures the time taken by the bus for every kilometre. The driver notices that the bus travels 1 kilometre every 2 minutes.

Data Table

He prepares the data table after this so that he has a clear understanding of everything and then draws the graph as shown below.

By this table, he had a clear idea about the speed which is: ½ × 60 = 30 km/hr.

The graph is a straight line and the motion of the bus is also uniform. Also, from the graph, we can find the speed of the bus at any instant of time. The initial and final position of the car can be found as the following:

Speed = (Final Position-Initial position)/Time

The slope of the line can be found by drawing a rectangle anywhere near the straight line which determines the speed of the bus. If an object is not moving, the distance-time graph results in a horizontal line which shows that the object is at rest.

Conclusion:

The following things can be concluded now:

• If the distance-time graph is a straight line then the motion is uniform.
• If the distance-time graph of a body is given, its speed can be calculated using the slope of the graph.
• The slope of the straight-line graph is the same irrespective of the interval which is chosen. This implies that the speed of an object under uniform motion remains constant.

What is Velocity -Time Graph and Displacement-Time Graph?

A graph is defined as a pictorial representation of information which is a two-dimensional drawing showing the relationship between dependent and independent variables. Independent variables are denoted on the horizontal line known as the x-axis, while the dependent variables are denoted on the vertical line known as the y-axis.

The main components of a 2D graph are x-coordinate and y-coordinate.

Displacement time graph, velocity-time graph, and acceleration time graph are three common types of graphs in classical mechanics.

In the distance-time graph, distance is the dependent variable and is represented on the y-axis, while time is the independent variable and is represented on the x-axis.

The slope of the distance-time graph represents the speed of an object.

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