ncert solutions for class 9th science chapter 8

1. Motion is related with movement of any object.
Mechanics is the branch of physics that deals with Motion of a body.
Before learning more facts about motion let us first understand what actually motion is:
Motion: An object is said to be in motion when it changes its position with respect to the surrounding at a
given period of time
Rest : An object is said to be in when it does not change its position during a time
Different types of motions are :
Linear motion : straight line motion
Circular motion: In circle format
oscillatory /vibratory : to and fro motion
Now let us move towards the important keywords. We will be using these terms frequently :
1. Scalar : This is a type of physical quantity having only magnitude and no directions
1. Vector : These are the physical quantities having magnitude and directions as well.

2. 3. Distance : The actual length of the path travelled by an object during its journey
from initial or starting point to final point is called distance travelled.Magnitude of
distance can never be zero or negative and the SI unit of distance is metre.
Distance is a scalar quantity (only magnitude).
4. Displacement : Displacement is the length of the shortest path between the
initial and the final point. The magnitude of displacement can be zero and negative
when the initial and final point coincide. The S.I unit of displacement is also metre.
Displacement is a vector quantity(both magnitude and directions). Displacement
will always be equal to less than the distance travelled

3. Types of motion:
Uniform motion: When a body travels equal distance in equal interval of time, it
is said Uniform motion.
The Time and Distance graph of uniform motion
Non-Uniform Motion : When the body cover unequal distances in equal time
intervals.
The graph of this motion is curved line.
Non-uniform motion is further divided into:
Accelerated and De -accelerated motion

4. Now let us understand some facts about speed and other terms related to it.
Speed --- We can get speed by the ratio of Distance and Time. It’s S.I unit is m/s.
Speed (s) = Distance (d)/Time (t)
Speed is the measure of total distance covered per unit time.
Speed can be uniform or non-uniform.
Average Speed = Total distance travelled / total time taken
=(d1+d2+d3+dn) / (t1+t2+t3+tn)

5. Velocity
It is the measure of speed or change in speed in specific unit of time. It is a vector
quantity.
Mathematically , velocity = displacement / time
Velocity is a vector quantity and its S.I. unit is m/s.
Average displacement will be calculated as
Average velocity = (initial velocity + final velocity) / 2 = (u+v) / 2
OR = total displacement / total time
Velocity can be positive, negative or zero

6. Acceleration:
It is the rate of change of velocity per unit time. It is observed in non- uniform
motion.
Mathematically, acceleration = final velocity - initial velocity / time
= (v-u) / t
If acceleration “a” is positive then it symbolizes that speed/velocity is increasing
with time
If acceleration is negative, it is called retardation and symbolizes that
speed/velocity is decreasing with time

7. Graphical representations:
1. Speed vs time graph for uniform motion and non - uniform motion.
Acceleration slope retardation slope
The slope of graph gives the value of velocity

8. 2. Speed vs Time graph for body at rest:
Here, S1= S2.
Therefore v=(s1- s2)/ (t1-t2) = 0.

9. Velocity - time graph for uniform motion,
Since, v1 = v2. This means that v1-v2 = 0.
This indicates that this motion is not changing velocity and hence has no
acceleration

10. Velocity- time graph for uniformly accelerated motion
Acceleration (a) = (v2-v1) / t2-t1.
Since it is a uniformly accelerated motion, hence the value of a will be same
throughout the motion or at any point of the graph.

11. Velocity-time graph for the non uniformly accelerated motion
In this scenario, there is no constant change in velocity. V2 is not equal to V1.
Therefore acceleration is not same at any point of the motion.

12. Velocity - time graph for a retarded or uniformly de-accelerated motion.
The graph is a downward slope, which makes the decrease in speed and velocity.

13. Velocity time graph for non - uniformly de-accelerated motion
This decreasing or downward moving curve shows that speed is decreasing non-
uniformly with time slot

14. Equation of Motion:
In this section we need to study the three equation of motion . We will be using
these equation later to solve the numericals in this chapter.
1) v = u+at
2) s=ut+½(at^2) [ time raised to power 2]
3) v^2 - u^2 = 2as
v= final velocity ; u = initial velocity; a = acceleration; s = distance completed;
t= time taken

15. Graphical Representation:
Let a body be at point having initial velocity u = 0 m/s (i.e; body is at rest).
Body attains final velocity v at certain time ‘t’ and reaches point B.
First equation of motion
a= change in velocity/total time taken
= (OB-OA) /(OC-O) = (v-u) / (t - 0)
= (v - u)/t
v= u+ at

16. Second equation of motion
Distance travelled by object = Area of OABC (it is a trapezium)
Area of rectangle OADC + area of triangle ABD
S = (OA x AD) + ½ xAD xBD
= u x t + ½ X t x (v-u)
=ut + ½ t Xat
S =ut + ½ at^2

17. Third equation motion:
Distance travelled by body = Area of trapezium
s = (OA+BC) x OC / 2 [ using formula of area of trapezium]
= (u+v) x t / 2
= (u+v / 2) + (v-u / a) [ using v = u +at]
s = v^2 - u^2 / 2a OR
v^2 - u^2 = 2as

18. Circular motion:
A type of motion in which body revolves around a centre point or in a circular
path with uniform speed is called circular motion.
The velocity in such motion is always tangent to the speed or the direction of the
motion. The velocity in such cases is different at different points.
Thus, uniform circular motion is accelerated motion.