Motion
CBSE Class 9 · Science · Notes, formulas and practice questions
Motion is the Class 9 physics chapter that explains how to describe moving objects using distance, displacement, speed, velocity, acceleration, graphs and the three equations of motion.
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Motion is the first chapter in physics that makes the idea of movement quantitative. It begins by separating distance from displacement: distance is the whole path actually travelled, while displacement is the straight-line change in position from start to finish. The chapter then sorts motion into uniform and non-uniform categories. These ideas are followed by definitions of speed, velocity and acceleration, where direction becomes important. Understanding scalar and vector differences here prevents most of the common mistakes in numerical questions.
Graphs carry much of the meaning of this chapter. In a distance-time graph, a straight line means uniform motion, and its slope equals the speed. In a velocity-time graph the slope equals acceleration, while the area under the graph represents displacement. These two graph-related ideas give us a physical picture of changing motion. Before using any formula, you should be able to draw the corresponding graph and explain what the slope and area show.
The three equations of motion are the backbone of problem solving. The first equation, v = u + at, links final velocity to acceleration and time. The second, s = ut + ½at², gives displacement after a time. The third, v² = u² + 2as, connects velocity and displacement without needing the time. They are valid only for uniformly accelerated motion along a straight line. You should read each equation as a sentence, not as a symbol puzzle, and learn how its geometry comes from the velocity-time graph.
Uniform circular motion closes the chapter. Here an object moves around a circle with a steady speed, yet because the direction of velocity turns continuously, the motion is always accelerated. For one complete round, speed is circumference divided by time. This chapter therefore connects definitions, graphs and equations into one toolkit for describing everyday motion. Practising graph-based and formula-based numericals together is the surest way to master it.
Key terms
- Distance
- Distance travelled is the total length of the path an object covers while moving. It is a scalar quantity, so it has magnitude only and is always positive for motion. Its SI unit is metre (m).
- Displacement
- The shortest straight-line distance between the initial and final positions of an object, together with the direction of that line. It is a vector quantity, and it can be positive, negative or zero. An object returning to its starting point has zero displacement even if it has travelled a long distance.
- Uniform and non-uniform motion
- Uniform motion means that an object covers equal distances in equal intervals of time, however small the intervals are taken; in straight-line uniform motion the speed is constant. Non-uniform motion means the distances covered in equal time intervals are not equal, so the speed changes.
- Speed
- The distance covered by an object in unit time. For uniform motion, speed = distance/time. Average speed is total distance travelled divided by total time taken. Speed is a scalar quantity and is always non-negative.
- Velocity
- The displacement of an object in unit time; velocity = displacement/time. It is a vector quantity, so both its magnitude and direction matter. A body moving on a circular path at uniform speed has constant speed but continuously changing velocity.
- Acceleration
- The rate at which velocity changes with time. It is calculated as change in velocity divided by time: a = (v − u)/t. Acceleration is a vector quantity. When velocity decreases, acceleration is negative and is also called retardation.
- Distance-time graph
- A graph of distance travelled on the y-axis against time on the x-axis. For uniform motion the graph is a straight line, and its slope gives the speed. For non-uniform motion the graph is curved, and the slope at any point gives the speed at that instant.
- Velocity-time graph
- A graph with velocity on the y-axis and time on the x-axis. In uniform acceleration the graph is a straight line; its slope equals acceleration. The area enclosed between the graph line and the time axis equals the displacement of the object during that time interval.
- Uniform circular motion
- Motion of an object along a circular path with a constant speed. Because the direction of motion keeps changing, the velocity keeps changing, so the motion is always accelerated even though its speed does not change. For one complete revolution of radius r in time T, the speed is 2πr/T.
Formula sheet
| What | Formula | Notes |
|---|---|---|
| Speed (uniform motion) | v = d/t | v = speed, d = distance travelled, t = time taken. Speeds are in m/s when distance is in metres and time is in seconds. |
| Acceleration | a = (v − u)/t | u = initial velocity, v = final velocity, t = time interval, a = acceleration. A negative value of a means retardation. |
| First equation of motion | v = u + at | u = initial velocity, v = velocity after time t, a = uniform acceleration, t = time. It is valid only for straight-line motion with constant acceleration. |
| Second equation of motion | s = ut + ½at² | s = displacement after time t, u = initial velocity, a = uniform acceleration. It gives the displacement for uniformly accelerated straight-line motion. |
| Third equation of motion | v² = u² + 2as | u = initial velocity, v = final velocity, a = uniform acceleration, s = displacement. This equation is useful when the time of travel is not given. |
| Speed in uniform circular motion | v = 2πr/T | v = uniform speed along the circular path, r = radius of the circle, T = time taken for one complete revolution. The numerator 2πr is the circumference of the circle. |
Practice questions with answers
1. What is distance? What is displacement? How are they different?
Distance is the total length of path covered and is always a positive scalar quantity. Displacement is the shortest straight-line distance between the starting and final points, with direction, and is a vector quantity. If an object returns to its starting point, its displacement is zero while the distance covered is not.
2. Give an important difference between speed and velocity with an example.
Speed is a scalar quantity with only magnitude, while velocity is a vector quantity with both magnitude and direction. A car moving around a curve at a steady 40 km/h has constant speed but changing velocity, because its direction changes continuously.
3. State the SI unit of acceleration and write the formula that defines it.
The SI unit of acceleration is metre per second squared (m/s²). Acceleration is the change in velocity divided by time: a = (v − u)/t, where u is the initial velocity and v is the final velocity after time t.
4. A person walks 3 km north and then 4 km east. Find the total distance walked and the final displacement.
Total distance walked = 3 + 4 = 7 km. Displacement is the shortest straight-line distance from start to finish, so by Pythagoras it is √(3² + 4²) = 5 km. The direction is about 53° east of north.
5. A car accelerates uniformly from rest and reaches a velocity of 30 m/s in 10 s. Find its acceleration and the distance covered in this time.
Here u = 0, v = 30 m/s and t = 10 s. Acceleration a = (30 − 0)/10 = 3 m/s². Distance covered s = ut + ½at² = 0 + ½ × 3 × 10² = 150 m.
6. A motorcycle moving at 54 km/h applies brakes and stops in 3 s. Calculate the retardation and the distance travelled before stopping.
u = 54 km/h = 15 m/s, v = 0 and t = 3 s. Acceleration a = (0 − 15)/3 = −5 m/s², so retardation is 5 m/s². Distance s = ut + ½at² = 15 × 3 + ½ × (−5) × 9 = 45 − 22.5 = 22.5 m.
7. What information do you get from the slope and from the area under a velocity-time graph?
The slope gives acceleration, because acceleration equals change in velocity divided by time. The area enclosed between the graph and the time axis gives the displacement during that time. If acceleration is uniform, the graph is a straight line and the area can be found using simple triangle and rectangle formulae.
8. A bus goes from station A to station B at 40 km/h and returns along the same route at 60 km/h. Find its average speed for the whole journey.
Let the distance between A and B be d. Total distance covered is 2d. Total time = d/40 + d/60 = (3d + 2d)/120 = 5d/120 = d/24 hours. Average speed = 2d ÷ (d/24) = 48 km/h, not 50 km/h.
9. A cyclist completes two rounds of a circular track in 44 s. The radius of the track is 35 m. Taking π = 22/7, calculate the speed of the cyclist.
One round covers circumference = 2πr = 2 × 22/7 × 35 = 220 m, so two rounds cover 440 m. If two rounds are completed in 44 s, then speed = 440/44 = 10 m/s.
10. Why is an object in uniform circular motion accelerated even when its speed is constant?
In uniform circular motion the magnitude of velocity, which is speed, does not change, but its direction changes continuously. Since velocity is a vector quantity, any change in direction is a change in velocity. Acceleration is the rate of change of velocity, so the motion is accelerated, with acceleration directed towards the centre of the circle.
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