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## Chapter: Motion

In everyday life, we see some objects at rest while others in motion. Birds fly in the sky, fish swim in water, blood flows through the veins and arteries of the human body. All things including atoms, molecules, planets, stars and galaxies are all said to be in motion. We can say that when the position of an object changes with respect to its surrounding with the passage of time, then the object is said to be in motion. In some cases, we directly don’t see motion but can feel it. Have you ever seen air? How do you know it’s moving / blowing? We don’t see it but we feel it by seeing the movement of the branches of trees, paper etc. Have you ever thought what causes the phenomena of sunrise, sunset or changing of seasons? Is it due to the movement of the earth? If it is true, then why don’t we directly feel the motion of the earth?

Most of the motions are termed to be complex. Some objects move in a straight line and some move in a circular path. Some rotate and some vibrate. In addition, there may be some situations involving a combination of all these. We use simple equations and graphs to express the various types of motion.

## Describing Motion

A reference point is used to describe the location of an object. Let us say our school is around 5km south of the shopping mall. In this case, shopping mall is taken as the reference point. We can choose reference points as per our convenience. So we can conclude that some reference point is required to describe the position of any object. This reference point is called origin.

## Motion along a Straight Line

The simplest type of motion is the one along a straight line. Let us take an example and consider that the object is moving along a straight path. O is the starting point from which the object starts moving. Hence O is called as the reference point. Consider A, B and C as position of the objects at different intervals. C is the point where the object reaches first, and then it moves to B and finally reaches A. Again it moves back through the same path and passes through B and reaches C.

Positions of an object on a straight line path.

We can see that the total length of the path covered by object is OA + AC that is 60 km + 35 km = 95 km. This is called the distance covered by the object. We specify distance in a numerical value and not the direction of motion. Distance and Displacement are the two different physical quantities that are used to describe the overall motion of an object. They are also used to locate the object’s final position with reference to its initial position at a given time in particular.

### Distance and Displacement:

Distance is the actual length of the path covered by a body between two points, while displacement is the shortest length of the path between two points. Distance is scalar quantity i.e. it has magnitude only while displacement is a vector quantity, which has both magnitude and direction.

## Uniform Motion and Non Uniform Motion

Uniform Motion:– When an object covers equal distance in an equal interval of time, the motion is called uniform motion. For example – if a moving vehicle covers a distance of 10 km every hour, the motion of the vehicle is called uniform motion.

Non-Uniform Motion:- When an object covers unequal distance in an equal interval of time, the motion is called non-uniform motion. For example – If a moving vehicle covers a distance of 10 km in the first hour, then covers a distance of 20 km in the second hour and covers a distance of 5 km in the third hour, etc. the motion of the vehicle is called non-uniform motion.

### Speed:

Distance covered by a moving object in unit time is called speed.

Where, v = speed, s = distance, t = total time.

SI unit of speed is meter per second (m/s).

### Average speed:

Average speed is the ratio of total distance covered and total time taken.

Where, v = Average Speed, s = Total distance covered, t = total time taken. SI unit of average speed is meter per second (m/s).

## Speed With Direction

The rate of motion of an object can be more comprehensive if we specify its direction of motion along with its speed. The quantity that specifies both these aspects is called velocity.

### Velocity:

The speed of a moving object in particular direction is called velocity. Velocity has both magnitude and direction while speed has only magnitude and no direction.

Velocity of an object is the distance covered in particular direction in the unit of time.

SI unit of velocity is meter per second.

### Uniform velocity:

Uniform speed of an object in same direction is called uniform velocity.

### Non-Uniform velocity:

Velocity of an object is changed in following two conditions.

(a) When speed is changed

(b) When direction is changed

Thus, non uniform speed of a moving object in same direction, or non-uniform speed in different directions or uniform speed in different directions is called non-uniform velocity.

Example– If a vehicle is moving on a circular path with uniform speed, then its velocity is said to be non-uniform, because on a circular path the direction of a moving body changes along with the direction of the curve.

If a vehicle is moving with a uniform speed on a zigzag path, the velocity of the vehicle will be non-uniform because direction of a vehicle is changed with the change in the direction of path.

### Average Velocity:

The arithmetic mean of velocity of an object moving along a straight line is called the average velocity.

Where, u is the initial velocity and v is the final velocity.

The displacement of a moving object in unit time is also called the average velocity.

### Acceleration:

The rate of change in velocity is called acceleration. Acceleration is generally denoted by ‘a’.

Where, ‘a’ is acceleration, ‘v’ is final velocity, ‘u’ is initial velocity and ‘t’ is time taken for change.

A positive sign of the magnitude of acceleration shows increase in velocity and a negative sign show decrease in velocity. If there is decrease in acceleration, it is called Retardation. This means, the rate of decrease in the velocity is called Retardation.

### SI unit of acceleration:

The SI unit of velocity is meter /second. The SI unit of time is second.

## Graphical Representation of Motion:

Graphs provide a very feasible method of giving the basic information about a variety of events. For example, in any game, we use a graph to show the progress of the game between each team. A straight-line graph helps in solving a linear equation having two variables.

We can also use line graphs to describe the motion of an object. We can show the relation between one quantity like velocity or distance with respect to another quantity like time.

## Distance-Time Graph

The dependence of the position of an object with time can be shown on the following distance-time graph that is shown as below. We can take a convenient scale of choice. Here in the graph, time is taken along x-axis and distance is taken along y-axis. Distance-time graphs can also be used to describe various conditions where objects move with uniform speed, non-uniform speed, remain at rest etc.

Distance-time graph of an object moving with uniform speed

A graph of distance travelled against time is a straight line, as shown in the above figure.

Distance-time graph for a car moving with non-uniform speed

The nature of this graph shows nonlinear variation of the distance travelled by the car with time. Thus, the graph shown in the above figure represents motion with non-uniform speed.

## Velocity-Time & Graph

The variation in the velocity with time for an object moving in a straight line can be shown by a velocity-time graph. In this graph, time is shown along the x-axis and the velocity is shown along the y-axis. If the object moves at a uniform velocity, the height of its velocity-time graph will not change with time. It shall be a straight line parallel to the x-axis.

Velocity-time graph for uniform motion of a car

The velocity-time graph for the motion of a car is shown as in the figure below. The nature of the graph shows that the velocity changes by equal amounts at equal intervals of time. Thus, for all uniformly accelerated motion, the velocity-time graph is generally a straight line.

Velocity-time graph for a car moving with uniform accelerations

Velocity-time graphs of an object in non-uniformly accelerated motion

The above graphs represent a velocity-time graph. The first graph shows the motion of an object whose velocity is decreasing with time and the second graph represents the motion of an object with time with a non-uniform variation.

### Equations of uniformly accelerated motion:

Three equations are:

1. v = u + at
2. s = ut + 1/2 at2
3. v2 - u2 = 2as

Where, v = final velocity, u = initial velocity, a = acceleration, t = time

## Uniform Circular Motion

We can state that the object is accelerating if the velocity of an object changes. This change in the velocity is due to changes in its magnitude or the direction of the motion or sometimes both.

Let us consider an example where an object changes its direction of motion and not its magnitude of velocity.

Let us take the example of an athlete running in a closed path. The figure below shows the path of an athlete along a rectangular track ABCD. Now consider that the athlete runs at a uniform speed on the straight parts AB, BC, CD and DA of the track. He abruptly changes his speed at the corners, in order to keep himself on track. Try to count how many times will the athlete have to change his direction of motion by the time he completes one round? It is clear that he has to change his direction of motion four times to keep on moving in a rectangular track once.

The motion of an athlete along closed tracks of different shapes