# Chapter 8 Motion

## Class 9th Science: Chapter 8 Motion

### Introduction to Motion

If a body does not change its position with respect to time and the surroundings, it is said to be at rest and else it is said to be in motion. Motion of objects can take place along one direction, two directions or three directions at a time.

If an object moves along a straight path it is said to be linear or one-dimensional motion. If an object moves along two directions at a time like that of a ball hit for a sixer in a cricket, it is two-dimensional. The haphazard motion of a honey bee can be three-dimensional.

The change in position of an object is termed displacement. It requires both direction and magnitude for its complete description and hence such physical quantities are called a vectors. The length of the path covered by a moving body is its distance and is independent of direction. Thus, such physical quantities are called scalars.

The rate of distance covered by a body is its speed and is measured in metre per second in international units. If a body covers equal distances in equal intervals of time however small the intervals may be, it has uniform speed. If a body covers unequal distances in equal intervals or equal distances in unequal intervals then it is said be moving with non-uniform speed.
•  Speed is a scalar quantity.
•  Speed = distance travelledTime taken. .
•  A body is said to be moving with uniform speed if it has equal intervals of time, however small these intervals may be.
•  A body is said to be moving with non uniform speed  if it has unequal distances in equal intervals of time or equal distances in unequal intervals of time, however small these intervals may be.

Average speed:
•  Average speed = total distance travelledtotal time taken
•  Instantaneous speed = limt0stdsdt.
•  If a particle covers the 1st half of the total distance with a speed 'a' and the second half with a speed 'b'
Average speed =  2aba+b .
•  If a particle covers 1st 1/3rd  of the total distance with a speed 'a', 2nd  1/3rd of the distance with a speed 'b' and 3rd 1/3rd of the distance with speed 'c'
Average speed =  3abcab+bc+ca .
•  1 kmph = 518   ms-1 ; 1mph = 2215   fts-1
•  For a body with uniform speed, distance travelled = speed x time.

The rate of displacement of a body is its velocity and is measured in metre per second in international units. If a body has equal displacements in equal intervals of time however smaller the intervals may be, it is said to be moving with uniform velocity. If the body is moving such that it has unequal displacements in equal intervals or equal displacements in unequal intervals of time, it is said to be moving with non-uniform velocity. The ratio of total displacement to total time taken by the body gives its average velocity. The velocity of a body at a given instant is its instantaneous velocity.
•  Velocity is a vector quantity.
•  For a body moving with uniform velocity , the displacement is directly proportional to the time interval.
•  If the direction or magnitude or both of the velocity of a body change, then the body is said to be moving with non-uniform velocity .
•  Average velocity Net displacementTotal time taken
•  For a body moving with uniform acceleration, the Average velocity = u+v2.
•  The velocity of a particle at any instant of time or at any point of its path is called instantaneous velocity v⃗   =   limt0s⃗ t=ds⃗ dt   .

Average Velocity:
•  If a particular under goes a displacement s1 along a straight line t1 and a displacement s2 in time t2 in the same direction, then Average velocity = s1+s2t1+t2   .
•  If a particle undergoes a displacement s1 along a straight line with velocity v1 and a displacement ss with velocity  v2 in the same direction, then
Average velocity = (s1+s2)v1v2s1v2+s2v1   .
•  If a particle travels first of the displacement along a straigh line with velocity v1 and the next half of the displacement with velocity v2 in the same direction , then
Average velocity = 2v1v2v2+v1  (in the case(b) put s1 = s2)
•  If a particle travels for a time t1 with velocity v1 and for a time and for a time t2 with velocity v2 in the same direction, then
Average velocity = v1t1+v2t2t1+t2    .
•  If a particle travels first half of the time with velocity v1 and the next half of the time with velocity v2 in the same direction, then
Average velocity = v1+v22   (in the case d put t1 = t2) .
•  Velocity of a particle is uniform if both it magnitude and direction remains unchanged.
•  Velocity of a body changes when magnitude or direction or both change.

Acceleration
The rate of change in velocity is called acceleration and is measured in metre per square second in the international system of units.
Acceleration, a = Final velocity - Initial velocityTime
Time

Note: The negative acceleration is termed as retardation.

Differences Between Distance and Displacement
 S.No. DISTANCE DISPLACEMENT 1. It is defined as the actual path traversed a body It is the shortest distance betweeen two points by between which the body moves. 2. It is a scalar quantity. It is a vector quantity. 3. It can never be a negative or zero. It can be negative, zero or positive. 4. Distance can be equal to or greater than displacement. Distance can be egaual to or less than distance. 5. Distance travelled is not a unique path between two points. Displacement is a unique path between two points. 6. The distance between two points gives full information of the types of path followed by the body. Displacement between two points does not give full information of the types of path followed by the body. 7. Distance never decreases with time. For a moving body, it is never zero. Displacement can decrease with time. For a moving body, it can be zero. 8. Distance in SI is measured in metre. Displacement in SI is measured in metre.

Differences Between Speed and Velocity
 S.No. SPEED VELOCITY 1. It is defined as the rate of change of distance. It is defined as the rate of change of displacement. 2. It is a scalar quantity. It is a vector quantity. 3. It can never be negative or zero. It can be negative,zero or posituve. 4. Speed is velocity without direction. Velocity is directed speed. 5. Speed may or may not be equal to velocity. A body may possess different velocities but the same speed. 6. Speed never decreases with time. For a moving body, it is never zero. Velocity can decrease with time. For a moving body , it can be zero. 7. Speed in SI is measured in ms-1 Velocity in SI, is measured in ms-1

### Graphical Representation of Motion

A graph is a pictorial representation of the relation between two sets of data of which one set is of dependent variables and the other set is of independent variables.

In a displacement-time graph, displacement is a dependent quantity, taken on the Y-axis and time is taken on the X-axis, as it is independent. If the position of an object changes with respect to the reference position and time, it is said to be in motion.

The velocity at any instant of time is called instantaneous velocity. A positive slope of velocity-time graph gives acceleration and a negative slope gives deceleration or retardation of the object.

For an object moving with uniform acceleration, we have the following equations of motion,

v = u + at

s= ut +½ at2

v2 - u2 = 2as

Sn= u+a(n - ½)

Where u = Initial velocity,
s = Displacement,
a = Acceleration,
t  = Time and
v = Final velocity
Sn = The displacement of the body in n th second
n = n th second

If an object moves along a straight path, it is in a linear motion. If an object covers equal angular displacements in equal intervals of time then it is said to be in uniform circular motion. If an object repeats its motion on the path in regular intervals of time than it is in periodic motion.

Displacement-Time Graph
In the displacement-time graph, the time is taken on X-axis and the displacement of body is taken on Y-axis. From this graph, we can determine the velocity of body. Since, velocity is the ratio of displacement and time therefore the slope of displacement-time graph gives the velocity. If the is positve, it implies that the body is moving away from the starting point.

If a body moves in a straight path the distance and the displacement of the motions are equal so the Displacement - Time graph and the Distance - Time graph are same.

(i) If the graph is parallel to time axis, then body is stationary.

(ii) If graph is a straight line, making an angle with the vertical axis i.e., Time axis  then body is moving with a uniform velocity. The velocity can be found out by finding the slope of the graph.

(iii) The graph can never be parallel to displacement axis, as it means that displacement increases indefinitely, with out any increase in time, which is impossible.
(iv) If graph is a curve, it means the body is moving with a variable velocity, and hence has some acceleration.

Velocity-Time Graph

In the velocity-time graph, time is taken on X-axis and the velocity is taken on Y-axis. Since velocity is a vector quantity, the positive velocity means that the body is moving in a certain direction away from its initial position and the negative velocity means that the body is moving in opposite direction.

(i) If Velocity-Time grapgh lies on the  X -  axis as the following

(a) it represents a body is at rest.
(b) Its acceleration is zero.

(ii) If Velocity-Time grapgh is parallel to time axis,

(a) Body is moving with uniform velocity.
(b) Its acceleration is zero.
(c) Its displacement can be found by finding the area of the graph.

(ii) If Velocity-Time grapgh is a straight line making an angle with time axis, as the following

(a) Body is moving with variable velocity.
(b) Its has uniform acceleration, which can be found by the slope of graph.
(c) Displacement can be found, by finding area under the velocity-time graph.
(d) If slope is positive, then the body has positive acceleration and vice-versa.
(e) If slope is negaitive, then the body has negative acceleration and vice-versa as shown in the following graph.

(iii) If the Velocity-Time grapgh is a curve,

(a) The body has variable velocity and variable acceleration.
(b) Area under the curve represents displacemet.
(c) Acceleration at aby instant can be found by finding slope at the point.

Acceleration-Time Graph
In the acceleration - time graph, time is taken on X-axis and acceleration is taken on Y-axis. From this graph, we can find the change in the speed in a certain interval of time. For linear motion , acceleration × time = change in speed, therefore the area enclosed between the acceleration - time sketch and the time axis gives the change in speed of the body.

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