## Motion and Time

Category : 7th Class

Learning objectives

1. Introduction
2. Slow and fast motion
3. Relation between distance and time: speed
4. Types of speed
• Uniform speed
• Non-uniform/variable speed
• Average speed
1. Time
2. Time measuring devices
• Sundial
• Sand clock/hour glass
• Water clock
1. Measuring of time using periodic motion: simple pendulum
2. Unit of time
3. Graph: Distance versus time

INTRODUCTION

The famous scientist Albert Einstein said "Nothing in the universe can be at absolute rest". This means that all objects are executing some types of motion. A body is said to be in motion whenever it changes its position with respect to its surroundings. When a body is in motion there is often a need to measure the quality of this motion with respect to time. Measuring time is of great importance to each one of us. How often in a day we check the time on a watch or clock? We need to know when it is time to attend a dance class, to catch the school bus, and many other such daily life activities.

SLOW AND FAST MOTION

The distance moved by objects in a given interval of time can help us to decide which object moves faster or slower than the other. Speed is refered to decide when object is slower or faster than the other. When two bodies move through same distance the faster one will take less time. When this distance is given in a particular direction it is known as displacement. The S.I. unit of distance or displacement is metre (m).

Do you know?

Cheetah is the fastest animal on the earth. It can accelerate from 0to 72 km/h in 3 seconds.

RELATION BETWEEN DISTANCE AND TIME: SPEED

In everyday life we see many objects which are moving like vehicles on the road, boats in the river, aero planes in the sky, etc. We need to measure their speeds. You would have seen that some vehicles have speedometer, which tells you how fast the vehicle is travelling.

Do you Know? The maximum recorded speed ever is the speed of light which is 3

Speed is defined as the distance travelled per unit time. When the quality of direction is added to the speed of moving object, then the body is said to have velocity.

Mathematically speed can be written as,

Speed is a scalar quality while velocity is a vector quantity. The S.I. unit of speed or velocity is meter/second or m/s. The other units are km/h, km/min etc. The rate of change of velocity is called acceleration.

TYPES OF SPEED

Uniform Speed

When a body travels equal distance in equal intervals of time, the speed of the body is said to be uniform speed.

Example: A car travels 10 meters in every one second, thus the speed of car is 10 m/s and is uniform.

Do you know? Earth moves round the sun with uniform speed

Non-Uniform Speed/Variable Speed

When a body travels unequal distance in equal intervals of time, the speed of the body is said to be non-uniform speed. Sometimes speed of the body increases while sometimes it decreases. When the speed of the body increases, then the amount by which the speed increases per second is called acceleration. When the speed of the body decreases then the amount by which the speed decreases per second is called retardation. The S.I. unit of acceleration or retardation is m/s2.

Example: If a car travels 10 meter in first 2 seconds, its speed is 10/2 =5 m/s, again it travels 20 meter in next 2 seconds, its speed is 20/2 = 10 m/s, thus the speed of car is non -uniform.

Instantaneous Speed

The speed of a body in motion at a particular instant is called instantaneous speed. An instant can be as small a time as possible. The instantaneous speed is given by

${{\text{S}}_{\text{inst}}}\text{=}\underset{\text{ }\!\!\Delta\!\!\text{ t}\to \text{0}}{\mathop{\text{Lim}}}\,\frac{\text{ }\!\!\Delta\!\!\text{ d}}{^{\text{ }\!\!\Delta\!\!\text{ t}}}$

Note: - An odometer or hodograph is an instrument that indicates distance travelled by a vehicle, such as automobile. The device may be electronic, mechanical or combination of the two.

Average Speed

The average speed of a body is total distance travelled by the body by total time taken to cover this distance.

The average speed is given by

${{\text{S}}_{\text{av}}}\text{=}\frac{\text{Totaldistancetravelled}}{\text{Total time taken to cover this distance}}$

Example: If a car travels a distance of 200 km in 5 hours, the average speed is 200/5 = 40 km/h. This does not mean that the car is moving at this speed all the time.

Do you know? Electricity is conducted through the wire at a speed 15,000 km/s, but the nerve impulse in our body travels at a maximum speed of about 100 m/s only.

TIME

Time is the lapse between the regularly recurring events. References of time are given as "Anti Meridiem (A.M.)", "Post Meridiem (P.M.)" "Before Christ (B.C.) and "AnnozDomini (A.D.)".

TIME MEASURING DEVICES

In ancient time some devices used to measure short time duration.

These are:

Sundial

Sundial is based on the fact that the position and length of shadow cast by an object. Changes with the time during the day. It consists of a horizontal circular board with a triangular plate of metal which is fixed vertically on it and kept along north-south direction. The plate casts its shadow on the board. The edge of the shadow falls at different angles during different times of the day. The position of the shadow is utilized to mark the time of the day.

Sand Clock/ Hour Glass

Sand clock is made up of two rounded glass bulbs which are connected by a narrow neck of glass. It is based on the principle that sand from the upper glass bulb falls into the lower glass bulb in a fixed time so it became the unit of time.

Do you know? The national physical laboratory, an institute in New Delhi, maintains standard measurement (such as meter, kilogram, second, etc.) for our country

Water Clock

Water clock is based on the principle of regulated flow of water. In this device time taken for the container to empty up to different levels was measured.

MEASURING THE TIME BY USING PERIODIC MOTION:

SIMPLE PENDULUM

The motion that repeats itself at equal intervals is called Periodic motion. This process is used to measure time interval by clocks and watches.

Simple Pendulum

A simple pendulum consists of a long, fine, weightless string and a weight tied to one end of the string called a bob of the pendulum and the other end is attached to a rigid support.

Note: - The most accurate of all clocks are atomic clocks, which will lose or gain just one second every 300,000 years.

Time Period of a Simple Pendulum

The time taken to complete one oscillation is called the time period of the pendulum. Time period depends upon the length of string from which bob is suspended. It is observed that for a particular pendulum length, the time period does not change and it is taken as constant. This observation led to the development of pendulum clocks. Wall clocks, wrist watches were refinements of the pendulum clocks.

UNIT OF TIME

The S.I. unit of time is second(s) but different units of time are used depending on the need. Days and years are natural time units. Earth spins once a day and moves around the sun once a year.

1 mean solar day = 24 hours

= 24 x 60 minutes

= 24 x 60 x 60 seconds

= 86,400 seconds

Prefix micro ($\mu$) is used for factor${{10}^{-6}}$. Second is the basic unit of time.

Other commonly used units of time are

1 week = 7 days

1 year = 365 days

100 years =10 decades = 1 century

1000 years =10 centuries = 1       millennium

For measuring very small time intervals as one millionth or one billionth electronic clocks are used.

Do you know? The system of units that scientists use in most of their work is called system international d’ unit’s (international system of units) abbreviated as SI units.

GRAPH

A graph is a pictorial representation of mathematical relationship between two physical quantities. A graph contains two axes - a horizontal axis, which is known as x-axis and a vertical axis, which is known as y-axis. The independent quantity is shown along x-axis and the dependent quantity is shown along y-axis as shown below:

Do you know? In the game of cricket the graph of number of over’s versus score, the number of over’s the independent quantity and score is dependent quantity.

Distance-Time Graph for Uniform Speed

For every 10s, distance travelled is 100 m, so the speed of vehicle is uniform.

Distance-Time Graph for Non-uniform Speed

For every 10s unequal distance of 100 m, 400 m, 300 m, 500 m respectively is travelled so the speed of vehicle is non-uniform.

Do you want? A more steeply inclined distance time graph indicates greater speed.

The slope of distance time graph gives the speed of the moving object. For uniform speed of vehicle, slope of distance-time graph is constant, so the speed of the moving object is said to be uniform whereas in graph for non-uniform speed of vehicle, the slope of distance-time graph is varying so the speed of the moving object is said to be non-uniform.

CONCEPT MAP

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