VARDAAN LEARNING INSTITUTE | POWERED BY VARDAAN COMET

Motion

CBSE Class 9 Science • Chapter 7 • Detailed Master Notes

Chapter Overview:

Motion is change in position of an object with time. This chapter introduces the concepts of distance, displacement, speed, velocity, and acceleration. We derive Equations of motion graphically and understand Uniform Circular Motion.

1. Distance and Displacement

Distance: Total path length covered by an object relative to a reference point. (Scalar quantity). Can never be zero for moving body.
Displacement: Shortest distance measured from initial to final position. (Vector quantity - has both magnitude and direction). Can be zero if initial and final positions are same.

2. Uniform and Non-Uniform Motion

Uniform Motion: Object covers equal distances in equal intervals of time. (Straight line graph).
Non-Uniform Motion: Unequal distances in equal intervals of time. (Curved graph).

3. Speed and Velocity

Speed ($v$): Rate of motion. Distance/Time. SI Unit: $m/s$. Scalar.

Velocity ($v$): Speed with direction. Displacement/Time. SI Unit: $m/s$. Vector.

Average Speed: $\frac{\text{Total Distance}}{\text{Total Time Taken}}$.

Average Velocity: $\frac{\text{Initial velocity (u) + Final velocity (v)}}{2}$.

4. Acceleration

Definition: Rate of change of velocity.

$$ a = \frac{v - u}{t} $$

SI Unit: $m/s^2$. vector.
Positive acceleration ($a>0$): Velocity increases.
Negative acceleration (Retardation, $a<0$): Velocity decreases.
Zero acceleration ($a=0$): Constant velocity.

5. Graphical Representation

(i) Distance-Time Graph ($s-t$):

Slope (Gradient) gives Speed.
Straight line = Uniform speed.
Parallel to time axis = Body at rest.

(ii) Velocity-Time Graph ($v-t$):

Slope gives Acceleration.
Area under curve gives Displacement.

6. Equations of Motion

For uniformly accelerated motion along a straight line.

1. First Equation (Velocity-Time relation):

$$ v = u + at $$

2. Second Equation (Position-Time relation):

$$ s = ut + \frac{1}{2}at^2 $$

3. Third Equation (Position-Velocity relation):

$$ v^2 - u^2 = 2as $$

Where: $u$ = Initial velocity, $v$ = Final velocity, $a$ = Acceleration, $s$ = Displacement/Distance, $t$ = Time.

7. Uniform Circular Motion

When an object moves in a circular path with uniform speed, its motion is uniform circular motion.

Direction changes continuously $\rightarrow$ Velocity changes continuously.
It is an accelerated motion.
Speed $v = \frac{\text{Circumference}}{\text{Time}} = \frac{2\pi r}{t}$.

Practice Zone

Q1: A bus decreases its speed from 80 km/h to 60 km/h in 5 s. Find acceleration.

Ans: $u = 80 \times \frac{5}{18} = 22.2 m/s$. $v = 60 \times \frac{5}{18} = 16.6 m/s$.
$a = \frac{v-u}{t} = \frac{16.6 - 22.2}{5} = \frac{-5.6}{5} = -1.12 m/s^2$. (Retardation).