# NCERT Solutions for Class 9 Science Chapter 8 Motion

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NCERT Solutions for Class 9 Science Chapter 8 Motion: Motion is a relative term. That is if we are travelling in a bus a person sitting behind us is at rest with respect to us but for a person outside the bus, he is moving. We feel like trees are moving when we are travelling in a bus, this is due to relative motion. We can find such enormous example related to motion. The NCERT Solutions for Class 9 Science Chapter 8 starts with the concept of reference point.  To specify the location of an object a reference point is necessary. For example, if a person tells my home is 60 Km north of the airport. Here the reference point is the airport. To specify the position of an object we need to choose a reference point and a direction. If in the previous case person tells my home is 60 Km from the airport then we can go 60 Km in any direction. To know the exact point specifying direction along with reference is also important.

Next topic of the chapter motion from NCERT Solutions for Class 9 Science is motion along a straight line. Here we will study the concept of distance and displacement. To understand the concept of distance and displacement mentioned in the NCERT Solutions let's consider an ant moving along a straight line. The ant starts from point O and moves a distance 50 cm and reaches point B, then it comes back a distance of 25 cm and reaches point A. We need to calculate the distance and displacement when the ant is at B and also when the ant is at A.

When the ant is at B the distance travelled = 50cm and displacement (shortest distance from the origin) = 50 cm. That is displacement = distance. When the ant comes back to A total distance travelled = OB+BA=50+25=75 cm but displacement = OA =25 cm. Here the displacement is less than distance. The main point to remember from this session of NCERT Solutions for Class 9 is that distance is always greater than or equal to displacement. The distance (path length) travelled cannot be zero but the displacement can be zero. In the above example of the ant comes back to O then displacement=0 but distance = 50+50 =100 cm.

The NCERT Solutions for Class 9 Science Chapter 8 Motion talks about uniform and non-uniform motion

Uniform motion: A motion of an object is said to be uniform if it travels equal distance in equal interval of time. That is a 10 m during the first second, 10m during next second, 10 m during 3rd second and so on. That is in each second the object covers a distance of 10 m.

Non-uniform motion: When an object travels different distance in equal interval of time the motion is said to be non-uniform. A car moving in a high traffic road will be non-uniform motion.

Next concept of the NCERT Solutions for Class 9 Science Chapter 8 is speed and velocity. Certain points to remember from this topic are listed below

• $Average \ speed = \frac{distance\ travelled}{total\ time\ taken}$
• If we specify the direction along with speed the term is known as velocity. Velocity is the speed of an object in a definite direction
• $Average \ velocity = \frac{displacement}{total\ time\ taken}$
• If the object is moving with varying velocity then the

$Average \ velocity = \frac{initial\ velocity+final\ velocity}{2}$

For example, if an ant moves along a rectangle as shown in figure 2 from point A to C through B in 5 seconds then what is the average speed and average velocity of the ant?

figure 2

Solution: The distance travelled by the ant = 3+4 =7m

average speed=7/5 = 1.4 m/s

The displacement = AC

$AC=\sqrt{AB^2+BC^2}=\sqrt{3^2+4^2}=5m$

AC is obtained using Pythagoras theorem

average velocity = displacement / total time taken= 5/5 =1 m/s

The next topic of the NCERT Solutions for Class 9 Science Chapter 8 Motion is acceleration:

• Acceleration is the rate of change of velocity
• $acceleration=\frac{change\ in\ velocity }{time\ taken}$
• The SI unit of acceleration is

$ms^{-2}or\ \frac{m}{s^2}$

• . The acceleration is taken to be positive if it is in the direction of velocity and negative when it is opposite to the direction of the velocity
• If an object travels in a straight line and its velocity changes by equal amounts in equal intervals of time, then the acceleration is uniform. If the change in velocity is not equal in equal interval of time then the acceleration is non-uniform
• The acceleration is positive in the direction of velocity and negative in the opposite direction of the velocity

The main topics of NCERT Solutions for Class 9 Science Chapter 8 Motion are listed below:

8.1 Describing Motion

8.1.1 Motion along a straight line

8.1.2 Uniform Motion and Nonuniform Motion

8.2.1 Speed with Direction

8.3 Rate of Change of Velocity

8.4 Graphical Representation of Motion

8.4.1 Distance- Time Graphs

8.4.2 Velocity-Time Graphs

8.5 Equations of Motion by Graphical Method

8.5.1 Equation for Velocity-Time Relation

8.5.3 Equation for Position-Velocity Relation

8.6 Uniform Circular Motion

NCERT Solutions for Class 9 Science Chapter 8: Distance time graph of an object moving with uniform velocity

Figure 3

The distance-time graph for an object moving with uniform velocity is a straight line. The speed of the object can be determined as follows

Consider a small portion AB on the line. Draw a line parallel to x-axis from A and a line parallel to y-axis. Let both the lines meet at C, then and mark the corresponding points of A, B and C as shown in the above figure. The points are s1,s2,t1 and t2

$speed=\frac{BC}{AC}=\frac{s_2-s_1}{t_2-t_1}$

NCERT Solutions for Class 9 Science Chapter 8 Motion: The velocity-time graph of an object moving with uniform velocity

figure 4

The graph of an object moving with uniform velocity is a straight line parallel to the x-axis. To find the distance travelled for a given time interval (say t2-t1 as in the above figure) we have to calculate the area of the velocity-time graph. That is in the above figure the area ABCD gives the distance travelled in time t2-t1.

NCERT Solutions for Class 9 Science Chapter 8 Motion: Velocity-time graph for a car moving with uniform acceleration

Figure 5

Velocity-time graph for a car moving with uniform acceleration is a straight line and the area of the graph gives the distance travelled during a time interval. In the above graph during t2-t1 the distance travelled= area of triangle ADE+area of rectangle ABCD.

An important topic of the NCERT Solutions for Class 9 Science Chapter 8 is equations of motion for an object moving with uniform acceleration. If the initial velocity is u, the final velocity is v and t is the time taken and s is the distance travelled then the following are the three equations of motion.

$\\v=u+at\\s=ut+\frac{1}{2}at^2\\v^2-u^2=2as$

NCERT Solutions for Class 9 Science Chapter 8: Uniform circular motion

Let's understand this through an example: If an ant moves along a circular path of radius 7 cm from point A to B through C and then to A through D as shown in figure 6 with a uniform speed of 1cm/sec

i)what is the distance travelled when the ant is at B. Is the distance equal to displacement?

Solution:

$distance=ACB=\frac{1}{2}circumferance=\frac{1}{2}\times2\pi r=\frac{1}{2}\times2\pi \times 7=22cm$

Displacement =AB=diameter =14cm. So distance not equal to displacement

ii)what is the total distance travelled and the final displacement?

Total distance travelled = circumference of the circle = $2\pi r=2\pi \times 7=44cm$

Displacement =0 as the initial and final position are the same

iii) What is the time taken by the ant to travel from A to B

The time = distance / speed = 22 / 1 = 22 sec

## NCERT Solutions for Class 9 Science- Chapter Wise

 Chapter No. Chapter Name Chapter 1 Matter in Our Surroundings Chapter 2 Is Matter Around Us Pure Chapter 3 Atoms and Molecules Chapter 4 Structure of The Atom Chapter 5 The Fundamental Unit of Life Chapter 6 Tissues Chapter 7 Diversity in Living Organisms Chapter 9 Force and Laws of Motion Chapter 10 Gravitation Chapter 11 Work and Energy Chapter 12 Sound Chapter 13 Why Do We Fall ill? Chapter 14 Natural Resources Chapter 15 Improvement in Food Resources

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