GRAPHS OF MOTION

INTRODUCTION

Can we describe motion using graphs?

Let us try with some situations.

• The distance travelled by an object in unit time such as hour, minute, second is called average speed of the object.

• The equation to calculate average speed is

• If we measure the distance in kilometers and the time in hours, the unit of speed will be kilometers per hour Or KMPH.

• We can use the other units of distance and time to measure speed such as:

• kilometer per hour, kilometer per minute, kilometer per second, meter per minute, meter per second etc.

Example:

A person travelled 15 kilometers in 3 hours.

Remember!

• It is necessary to mention the unit when we denote any quantity like distance, time, speed, weight etc.

• Otherwise it becomes meaningless.

• Therefore remember to write the unit after the quantity that you denote.

• There are different ways to describe journey.

• Let us explore to use graphs in describing a jouney.

• Look at the details of Ishan’s walking from his home to school.

• From this data, it is clear that Ishan travelled 120 meter for every consecutive two minute segments throughout his journey.

• That is he travelled equal distance of 120 meter in every consecutive two minute segments throughout his journey.

• But it does not tell us how far he walked at any given time of his journey, For example say after 9 minutes.

• To know the how far he walked after 9 minutes we need further calculation.

• Similarly, we cannot find the distance between her home and her school, just by looking at the given table.

• Therefore we must present the data in in a different way.

• We must calculate the total distance covered with respect to the total elapsed time as shown on the screen.

• Let us now use this data to make a graph of Ishan’s journey.

• For this we need to show the time taken on the horizontal axis and the distance covered on the vertical axis.

• The horizontal axis is known as time axis.

• The vertical axis is known as distance.

• Record the scale at the upper right corner of your graph paper.

• To represent the data from the table as a graph, mark the first point on the graph which corresponds to a time of two minutes on the X-axis and a distance of 120 meters on the Y-axis.

In the same way, plot the remaining five points on the graph paper.

• Connect these points using a ruler.

• This graph shows the journey of Ishan from his home to school.

• Graphs in this chapter are plotted for the time elapsed against the distance covered known as distance - time graphs.

Do a route map and a distance time graph give the same information?

Let us explore!

• Compare the graph that shows Ishan’s journey graph and the route map.

• A route map shows the road of the journey from Ishan’s home to school.

• Can you estimate how long Ishan takes to reach his school by looking at the map?

•  Can we guess the number of turns along the road from Ishan’s home to school from the map?

•  Can we guess where the road crosses the river, by looking at the graph?

• It is evident that the information you get from a route map cannot be obtained from a graph.

• Similarly, information about the speed at which Ishan walked can be obtained only from the graph, but not from the map.

• Can we find the distance covered by Ishan for every two minutes of interval of his journey from the graph?

• Did Ishan cover an equal distance in every two minutes interval of his journey?

• Let us Explore!

• If the distance time graph of a motion is a straight line, making an angle with the time axis.

• It does mean that the object is covering equal distances in equal intervals of time that represents a uniform motion.

• The distance time graph doe snot show the route of the journey.

• Therefore we can say that any graph of uniform motion will be a straight line.

• In other words if a graph of motion is a straight line it represents uniform motion.

• What is Ishan’s speed for each two minute segment of his journey.

• Ishan’s speed for each two minute segment of his journey is 120 meters.

• That is 60 meters per minute.

• What is the average speed of Ishan’s complete journey.

• The average speed of Ishan’s complete journey is also 60 meters per minute.

• Is the speed for each two minutes segment the same as his average speed for the entire journey?

• Yes, the speed of the journey for each two minutes segment is same as his average speed for the entire journey.

• In such cases the speed and the average speed are equal.

• Anish and Hitesh raced from their home to school.

• Activity 2

Graphs of objects moving at different uniform speeds

• They ran at uniform speeds.

• But their uniform speeds were different.

• Graph shown on the screen represents their motions.

• Can you say who ran faster, just looking at the graph?

• How much time did Hitesh take to run from home to school?

• Calculate the average speeds of both Hitesh’s and Anish.

• To answer these question we need to learn to read the Time-Distance graphs

Let us first explore the relation between speed of an object and slope of its graph of motion:

• Simply, we can compare the uniform speeds by comparing the slopes of the straight line graphs.

• The more the slope, the more is the speed.

• In another way we can compare the uniform speeds by comparing the angles made by the respective graphs with the time axis.

• The more the angle, the more is the speed.

Remember!

• This visual comparison is possible only between the graphs motion having the same scale.

Remember!

• We cannot compare graphs with different scales by just looking at them.

• Therefore Hitesh ran faster than Anish.

• Activity 3

Graphs of Stationary Objects

Look at the data of a trip recorded by a girl

Can you say by looking at the table whether the girl rested somewhere during her journey?

After walking how many minutes did the girl take rest?

For how many minutes did she take rest?

To understand how this is to be done, let us draw a graph of the girl’s journey.

But before we do this we must rearrange the figures in the table and write them in the way we did earlier.

Fill the blanks in the table shown on the screen.

• Using the data draw a graph of representing the journey of Bhoomika.

How far did Bhoomika travel after 12 minutes?

• From the 8th to 12th minutes of her journey, the time increased but the total distance covered remained same.

Bhoomika travel 420 m after 12 minutes

• When any object stops at a place, the time continues to increase but the distance covered does not change during its journey.

• This shows that the object is at rest.

• If we plot a graph for this data the graph line remains parallel to the time axis.

SUMMARY

• Motion is relative. Motion of an object depends on the observer.

• Distance is the path length traversed and displacement is the shortest distance in a specified direction.

In this chapter you have learnt:

• Speed at an instant is instantaneous speed which gives the idea of how fast the position of the body changes.

• Velocity is speed in specified direction.

• The motion is uniform when the velocity is constant.

• Average speed is distance covered per unit time and average velocity is displacement in a specified direction per unit time.

• The motion is said to be uniform accelerated motion if acceleration is constant .

• The equations of uniform accelerated motion are given by

V= u + at

v² – u² = 2as

• A body has acceleration when the velocity of the body changes.

• Acceleration is the rate of change of velocity

Based on dimensions

MOTION

Definition: The change in position of the body w.r.t time and surroundings

Nature

Acceleration: The rate of change of velocity of a body

One dimensional

Two dimensional

Three dimensional

Translator

Rotatory

Vibratory

Uniform acceleration: If equal changes in velocity takes place in equal intervals of time, however small the time intervals maybe.

Non-uniform acceleration: If unequal changes in velocity takes place in equal intervals of time.

Negative acceleration: If the velocity of the body gradually decreases w.r.t time, then acceleration is said to be negative acceleration.

Equation of motion for a body moving with uniform acceleration

Graphical representation

Distance: The total length of the path covered by the body

Displacement: The shortest possible distance from the initial and the final positions of the body

Speed: The distance travelled by the body in unit time

Velocity: The time rate change of displacement.

Average Velocity: The ratio of the total displacement to the total interval of time of a body.

Non-uniform or variable velocity: If a body covers unequal displacements in equal intervals of time or equal displacements in unequal intervals time.

Uniform velocity: If a body travels equal displacements in equal intervals time however small time intervals may be

Uniform Speed: If a body travels equal distances in equal intervals of time, however small these intervals may be, then it is said to be moving.

Non-uniform Speed: If a body travels unequal distances in equal intervals of time.

Average Speed: The ratio of the total distance travelled to the total time of travel.

Distance - Time

Speed - Time

Acceleration – Time

Horizontal line

Vertical line

Thank you…