Motion Class 9 Notes: Formulas, Graphs and Solved Examples

These motion class 9 notes cover the chapter “Describing Motion Around Us” from the new NCERT book. Motion is the base of physics, so every later topic, from force to energy, builds on it. First, learn the definitions and the difference between scalars and vectors. Then practise the three equations of motion and the graph rules, because most exam questions come from them.

Motion Class 9 Notes: Basic Ideas

An object is moving if its position changes with time. However, rest and motion are relative. A passenger sits still in a train, but a person on the platform sees the same passenger moving. Therefore, motion is always described with respect to a reference point, and absolute rest does not exist.

A point object is an object whose size is tiny compared to the distance it covers. For example, a train travelling between two cities can be treated as a point.

Scalar and Vector Quantities

A scalar quantity has magnitude only. Mass, time, distance, speed, work, energy and temperature are scalars. A vector quantity has both magnitude and direction. Velocity, acceleration, force, displacement and momentum are vectors.

Because vectors have direction, they follow special rules of addition. Scalars, on the other hand, follow ordinary algebra.

Distance and Displacement

Distance is the length of the actual path travelled. It is always positive, and it depends on the path. Displacement is the shortest straight-line distance from the initial position to the final position, with a direction. It can be positive, negative or zero, and it is the same for any path between two points. The formula is displacement = x_f − x_i.

Feature	Distance	Displacement
Meaning	Length of the path	Shortest distance with direction
Type	Scalar	Vector
Sign	Always positive	Positive, negative or zero
Moving body	Never zero	Can be zero
Comparison	Distance ≥ |displacement|	Equal only on a straight line

A circular track shows the difference well. After a quarter turn on a circle of radius r, the distance is πr/2 and the displacement is r√2. After a full circle, the distance is 2πr, but the displacement is zero.

Uniform and Non-Uniform Motion

In uniform motion, a body covers equal distances in equal intervals of time. In non-uniform motion, it covers unequal distances in equal intervals. For instance, a car on a clear highway at a steady speed shows uniform motion. A bus in city traffic shows non-uniform motion.

Speed and Velocity

Speed is the rate of change of distance, so v = s/t. It is a scalar and always positive. Velocity is the rate of change of displacement. It is a vector, and it can be positive, negative or zero.

Average speed equals total distance divided by total time. Average velocity equals total displacement divided by total time. Two special cases are useful. If a body covers equal distances at speeds u and v, the average speed is 2uv/(u + v). If it travels for equal times at speeds u and v, the average speed is (u + v)/2.

To convert units, remember that 1 km/h = 5/18 m/s, and 1 m/s = 18/5 km/h. As a result, 36 km/h equals 10 m/s.

Acceleration

Acceleration is the rate of change of velocity: a = (v − u)/t. Its SI unit is m/s². When velocity increases, the acceleration is positive. When velocity decreases, the acceleration is negative, and it is called retardation or deceleration. In uniform acceleration, the velocity changes by equal amounts in equal intervals of time.

Equations of Uniformly Accelerated Motion

For motion in a straight line with constant acceleration, let u be the initial velocity, v the final velocity, a the acceleration, t the time and s the displacement. The three equations are:

1. v = u + at, which links velocity and time.
2. s = ut + ½at², which links displacement and time.
3. v² = u² + 2as, which links displacement and velocities.

Choose the equation that does not contain the quantity you do not need. Also take care with signs: use a negative a for a body that slows down.

Solved Examples

Example 1. A car starts from rest and accelerates at 2 m/s² for 5 s. Find its final velocity and the distance covered.

Here u = 0, a = 2 m/s² and t = 5 s. Then v = u + at = 0 + 2 × 5 = 10 m/s. Also, s = ut + ½at² = 0 + ½ × 2 × 25 = 25 m.

Example 2. A train moving at 20 m/s brakes with a = −4 m/s². Find the distance it needs to stop.

Here u = 20 m/s, v = 0 and a = −4 m/s². Using v² = u² + 2as, we get 0 = 400 − 8s, so s = 50 m.

Graphical Representation of Motion

A distance-time graph shows how distance changes with time. A line parallel to the time axis means the body is at rest. An inclined straight line means uniform motion, and its slope gives the speed. A curved line means non-uniform motion.

A velocity-time graph shows how velocity changes with time. A line parallel to the time axis means uniform velocity, so the acceleration is zero. An inclined straight line means uniform acceleration, and its slope gives the acceleration. Moreover, the area under the graph gives the distance travelled.

Uniform Circular Motion

In uniform circular motion, a body moves on a circle at constant speed. Its direction changes at every instant, so its velocity is not constant. Hence, the motion is always accelerated. The speed on a circular path is v = 2πr/t, where t is the time for one round.

Common Mistakes in Motion Problems

• Students use distance in place of displacement, so they get the wrong sign.
• Many forget to convert km/h to m/s before they use the equations.
• Some apply the equations of motion when the acceleration is not constant.
• Others write the average speed as the simple mean in every case, although it holds only for equal times.

How to Revise This Chapter

Start with the definitions table. Next, learn the three equations and solve five numericals for each. After that, draw each graph by hand and write what its slope and area mean. Finally, solve the NCERT questions without looking at the answers. For the first chapter of the same book, read class 9 science chapter 1. You can also browse the Class 9 Science category and the Class 9 notes hub, or compare it with class 12 physics notes.

Wrap-Up

Motion class 9 notes work best when you pair each formula with a solved numerical and a graph. Revise the definitions daily, and practise units and signs. Then continue with the Class 9 Science category, or return to the The Note homepage.