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Class 9 Physics Chapter 7 Motion — Formulas & Key Points

Class 9 Physics Chapter 7 Motion is the gateway to mechanics and one of the highest-weightage chapters in CBSE board exams and competitive tests. This formula sheet compiles every equation, definition, unit and sign convention from the NCERT textbook into tables for quick revision. Whether you are solving numerical problems, preparing for term exams or brushing up before a test, this page gives you the entire chapter on one screen.

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Key takeaways

✓Motion is change in position with time; always measured relative to a reference point or observer.
✓Distance (scalar) is total path length; displacement (vector) is shortest straight-line distance from start to finish.
✓Speed is distance per unit time (scalar); velocity is displacement per unit time (vector) and includes direction.
✓Acceleration is rate of change of velocity; positive acceleration is speeding up, negative (retardation) is slowing down.
✓Three equations of motion (v = u + at, s = ut + ½at², v² = u² + 2as) apply only to uniformly accelerated motion.
✓Always convert units consistently (km/h to m/s: multiply by 5/18; m/s to km/h: multiply by 18/5) before substituting in formulas.
✓Uniform circular motion has constant speed but changing velocity because direction changes continuously.

Complete Formula Table — All Motion Equations at a Glance

This table lists every formula from Chapter 7 Motion in NCERT Class 9 Physics. Each formula is presented with its name, the equation in symbols, the meaning of each symbol, SI units and when to apply it. Bookmark this table and refer to it while solving NCERT exercises, sample papers or previous year questions. Remember that the three equations of motion apply only when acceleration is uniform and constant throughout the motion. For non-uniform acceleration or circular motion, different approaches are needed. Always identify which quantity is unknown and which three are given, then pick the equation that connects those four variables. This systematic approach prevents formula confusion during exams and saves time.

Speed: v = s/t — where v is speed (m/s), s is distance (m), t is time (s). Use for scalar motion without direction.
Velocity: v = Δx/Δt — where v is velocity (m/s), Δx is displacement (m), Δt is time interval (s). Use when direction matters.
Average speed: v_avg = Total distance / Total time. Use for non-uniform motion; include rest periods in total time.
Average velocity: v_avg = Total displacement / Total time. Remember displacement can be zero even if distance is not.
Acceleration: a = (v - u)/t — where a is acceleration (m/s²), v is final velocity, u is initial velocity, t is time.
First equation of motion: v = u + at. Use when displacement is not involved.
Second equation of motion: s = ut + ½at². Use when final velocity is unknown or not needed.
Third equation of motion: v² = u² + 2as. Use when time is unknown or not needed.

Formula Reference Table with Usage Hints

The table below organises all formulas by topic area within the chapter. Each row tells you the physical quantity, its formula, all symbols with units, and a practical hint on when to use that formula. For example, use the first equation of motion (v = u + at) when you know initial velocity, acceleration and time, and you need to find final velocity. Use the third equation (v² = u² + 2as) when time is not given in the problem and you need to connect velocities with displacement and acceleration. In problems involving multiple stages of motion (like a car accelerating then moving uniformly then braking), apply the appropriate formula to each stage separately, then combine the results. Many students lose marks by using the wrong equation or forgetting to convert units before substituting, so double-check your formula choice and unit consistency every time.

Key Terms and Definitions for Quick Revision

Understanding definitions is as important as knowing formulas because CBSE often asks 'define' or 'distinguish between' questions worth 2-3 marks. Motion is the change in position of an object with respect to a reference point over time; it is always relative, meaning an object can be in motion relative to one observer and at rest relative to another. Distance is the actual length of the path traveled (a scalar with no direction), while displacement is the shortest straight-line distance between initial and final positions along with direction (a vector). Speed is the rate at which distance is covered (scalar), whereas velocity is the rate at which displacement changes (vector). Acceleration is the rate of change of velocity; it is positive when velocity increases, negative (also called retardation or deceleration) when velocity decreases, and zero when velocity is constant. Uniform motion means equal displacements in equal time intervals regardless of the size of the interval; non-uniform motion means unequal displacements in equal intervals. Grasping these distinctions prevents conceptual errors in both theory and numerical questions.

Motion: Change in position of an object with respect to a reference point over time. Always relative to the observer or frame of reference.
Rest: An object is at rest if it does not change its position with respect to its surroundings over time.
Distance (s): Total path length covered by a moving object. Scalar quantity, always positive, SI unit is meter (m).
Displacement (Δx or s): Shortest straight-line distance from initial to final position, along with direction. Vector quantity, can be positive, negative or zero. SI unit is meter (m).
Speed (v): Distance covered per unit time. Scalar quantity. SI unit: m/s. Common unit: km/h.
Velocity (v): Displacement per unit time, with direction. Vector quantity. SI unit: m/s.
Acceleration (a): Rate of change of velocity. Vector quantity. SI unit: m/s². Positive if velocity increases, negative if decreases.
Uniform motion: Object covers equal distances (or displacements) in equal intervals of time, no matter how small the interval.
Non-uniform motion: Object covers unequal distances in equal time intervals. Most real-world motion is non-uniform.

Important Constants, SI Units and Sign Conventions

In numerical problems, using correct SI units is mandatory for full marks. Distance and displacement are measured in meters (m), though kilometers (km), centimeters (cm) and millimeters (mm) are also common and must be converted. Time is measured in seconds (s); convert minutes to seconds by multiplying by 60 and hours by multiplying by 3600. Speed and velocity are in meters per second (m/s), but many problems give data in km/h, which you must convert using the factor 5/18 (to go from km/h to m/s) or 18/5 (to go from m/s to km/h). Acceleration is always in m/s². Sign conventions are critical for vector quantities: choose one direction as positive (usually the direction of initial motion or rightward/upward) and the opposite as negative. If a body is slowing down, acceleration is opposite to velocity, so it carries a negative sign (retardation). For free-fall problems, acceleration due to gravity g = 9.8 m/s² or 10 m/s² (approximate) acts downward; assign it a negative sign if upward is positive. Mixing up signs is a top reason for wrong answers in motion numericals.

SI unit of distance and displacement: meter (m). Also used: km = 1000 m, cm = 0.01 m.
SI unit of time: second (s). Also: 1 min = 60 s, 1 h = 3600 s.
SI unit of speed and velocity: meter per second (m/s). Also: km/h. Conversion: 1 km/h = 5/18 m/s; 1 m/s = 18/5 km/h.
SI unit of acceleration: meter per second squared (m/s²).
Acceleration due to gravity (g): 9.8 m/s² or approximately 10 m/s². Direction: downward (assign negative if upward is positive).
Sign convention: Choose one direction as positive. Quantities in that direction are positive, opposite direction negative.
Retardation (deceleration): Negative acceleration. If a = -2 m/s², velocity decreases by 2 m/s every second.

Memory Tricks, Mnemonics and Quick Recall Tips

Remembering which equation of motion to use in which situation can be tricky under exam pressure. Here is a simple mnemonic: the first equation v = u + at has 'VUT' (sounds like 'what') — use it when you do not need displacement 's'. The second equation s = ut + ½at² includes 's' but not final 'v' — use it when final velocity is not required. The third equation v² = u² + 2as includes 's' and both velocities but not 't' — use it when time is not given. Another memory aid for unit conversion: to convert km/h to m/s, think 'divide by 3.6' (which is the same as multiply by 5/18). For the reverse, multiply by 3.6 (or 18/5). To recall that acceleration is rate of change of velocity, remember 'Acceleration Alters Velocity' (AAV). For average speed, remember it is NOT the arithmetic mean of two speeds unless time intervals are equal; always use total distance divided by total time. Finally, displacement can be zero even when distance is not zero (circular track, returning to start), so never confuse the two.

VUT mnemonic for v = u + at: 'VUT' (no 's') — use when displacement is unknown.
SUT mnemonic for s = ut + ½at²: includes 's' but no final 'v' — use when you do not need final velocity.
VUS mnemonic for v² = u² + 2as: includes both velocities and 's', no 't' — use when time is not given.
Unit conversion trick: km/h to m/s, multiply by 5/18 (or divide by 3.6). Reverse: multiply by 18/5 (or 3.6).
Acceleration sign: If slowing down, acceleration is opposite to velocity (negative if velocity is positive).
Average speed ≠ average of speeds. Always total distance ÷ total time, including rest periods.
Distance never decreases; displacement can decrease (if moving back toward start).

Common Sign, Unit and Notation Mistakes to Avoid

Students frequently lose marks due to avoidable mistakes in motion problems. One major error is forgetting to convert units before substituting into formulas; for example, using distance in km and time in seconds without converting km to meters will give a wrong answer. Always convert everything to SI units (m, s, m/s, m/s²) unless the question explicitly asks for km or km/h. Another common mistake is confusing distance with displacement; if a question says 'a car travels 100 km north then 60 km south', the distance is 160 km but the displacement is 40 km north. Do not use equations of motion for non-uniform acceleration; they apply only when acceleration is constant. Sign errors are rampant: if a body is thrown upward, initial velocity is positive and acceleration (gravity) is negative; mixing these signs will reverse your answer. Writing the answer without units or with wrong units costs marks; always write 'm/s' or 'km/h' next to your final numerical answer. Finally, do not round intermediate steps too early; keep at least two decimal places until the final answer to avoid rounding errors, especially in multi-step problems.

Forgetting unit conversion: Always convert km to m, hours to seconds, km/h to m/s before substituting in formulas.
Confusing distance with displacement: Distance is path length (always positive); displacement is straight-line separation (can be zero or negative).
Using equations of motion when acceleration is not constant: These three equations work only for uniform acceleration.
Sign mistakes: Choose a direction as positive, stick to it. Acceleration opposite to velocity is negative (retardation).
Omitting units in final answer: Speed = 15 is incomplete; write 15 m/s or 15 km/h. Units are part of the answer.
Using average of speeds instead of average speed formula: Average speed = total distance / total time, not (v₁ + v₂)/2 unless times are equal.
Early rounding: Keep two decimal places in intermediate steps; round only the final answer to avoid cumulative errors.
Not reading the question carefully: Check whether answer is wanted in m/s or km/h, distance or displacement, speed or velocity.

Solved Mini-Example 1: Speed and Unit Conversion

This example demonstrates how to handle unit conversion and apply the basic speed formula correctly. A frequent Board exam question type is: given speed in one unit and time in another, find distance in a third unit. The key is to convert everything to compatible units before applying the formula, then convert the answer to the required unit. Many students skip the conversion step and get wrong answers even though they know the formula. Practice these conversions until they become second nature. Remember: 1 km = 1000 m, 1 h = 3600 s, 1 min = 60 s, and the two main speed conversions are multiply by 5/18 (km/h to m/s) or 18/5 (m/s to km/h). Let us work through a complete example step by step, showing all conversions and units explicitly at every stage, exactly as you should write in your exam answer sheet to earn full marks and avoid silly mistakes that cost you grades.

Solved Mini-Example 2: Average Speed with Multiple Segments

Average speed problems confuse many students because they try to take the arithmetic mean of two or more speeds, which is incorrect unless the time intervals are exactly equal. The correct method is always: add up all the distances to get total distance, add up all the time intervals (including any rest or stop time) to get total time, then divide total distance by total time. This is a very common 3-mark or 5-mark question in CBSE Class 9 term exams and sample papers. The question might describe a journey in parts, for example a cyclist covers one part at one speed, rests, then covers another part at a different speed. You must carefully extract the distance and time for each segment, sum them up, and only then calculate average speed. Do not be tempted by the individual speeds; they are often red herrings. Focus on total distance and total time. Here is a worked example showing the complete method with all steps written out clearly, just as you should present your solution in the exam to score full marks and demonstrate clear understanding.

Solved Mini-Example 3: Applying Equations of Motion

The three equations of motion are the heart of this chapter and appear in almost every Class 9 Physics numerical problem set. Choosing the right equation is crucial. If the problem gives you initial velocity u, acceleration a, and time t, and asks for final velocity v, use v = u + at. If it asks for displacement s instead, use s = ut + ½at². If time is not mentioned at all, use v² = u² + 2as. A typical Board exam question will give you three out of the five variables (u, v, a, s, t) and ask you to find one or two others. First, write down what is given and what is to be found. Then identify which equation contains exactly those four variables. Substitute carefully, respecting signs: if the object is slowing down, acceleration will be negative relative to the initial velocity direction. Show all substitution steps and keep units throughout your working to avoid mistakes and to demonstrate clear method, which earns you method marks even if the final answer has a small error. Here is a complete worked example with all steps clearly shown, illustrating best exam technique.

One-Glance Last-Minute Revision Box for Exam Day

This revision box is designed to be read 10 minutes before your exam or test. It condenses the entire chapter into bullet points that you can quickly scan to refresh all formulas, definitions, units and key points. Print this section or screenshot it on your phone for quick reference during study breaks, on the bus to school, or right before entering the exam hall. The box covers every major formula, all important definitions, sign conventions, unit conversions, and the most common mistakes. If you have thoroughly practiced NCERT exercises and sample papers, this box will serve as a final confidence booster and memory trigger. Do not try to learn anything new from this box on exam day; use it only to recall what you have already studied. For deeper understanding and problem-solving practice, CBSETUTOR.ai offers 24×7 AI-powered doubt solving with photo upload at just ₹999/month, one flat price for Classes 6 to 12, with a 3-day free trial. Thousands of CBSE students use it to clarify tricky motion numericals and graph-based questions, getting instant step-by-step solutions any time of day or night, especially helpful before exams when coaching classes are closed.

Distance (s): total path, scalar, always positive, SI unit m. Displacement: shortest line, vector, can be zero, SI unit m.
Speed (v): s/t, scalar, SI unit m/s. Velocity (v): displacement/time, vector, SI unit m/s. Average speed: total distance/total time.
Acceleration (a): (v - u)/t, SI unit m/s². Positive = speeding up, negative = slowing down (retardation).
Three equations of motion (uniform acceleration only): (1) v = u + at, (2) s = ut + ½at², (3) v² = u² + 2as.
Choose equation based on unknown: no s → use (1); no v → use (2); no t → use (3).
Unit conversions: km/h to m/s multiply by 5/18; m/s to km/h multiply by 18/5. 1 km = 1000 m, 1 h = 3600 s, 1 min = 60 s.
Sign convention: pick one direction positive, opposite negative. Retardation is negative acceleration.
Common mistakes: not converting units, confusing distance with displacement, using average of speeds, omitting units, wrong signs.
Always write units in final answer. Show all steps for method marks. Check if answer is asked in m or km, m/s or km/h.
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Frequently asked questions

What is the difference between distance and displacement in Class 9 Physics Chapter 7?+

Distance is the total path length covered by an object, a scalar quantity always positive and measured in meters. Displacement is the shortest straight-line distance from the starting point to the final position, along with direction, a vector quantity that can be positive, negative or zero. For example, if you walk 3 m east then 3 m west, distance is 6 m but displacement is 0 m because you are back at the start.

How do I convert speed from km/h to m/s and vice versa?+

To convert km/h to m/s, multiply by 5/18 (or divide by 3.6). To convert m/s to km/h, multiply by 18/5 (or multiply by 3.6). For example, 72 km/h = 72 × 5/18 = 20 m/s. And 25 m/s = 25 × 18/5 = 90 km/h. Practice these conversions because they appear in almost every motion numerical problem in CBSE exams.

Which equation of motion should I use when time is not given in the problem?+

Use the third equation of motion: v² = u² + 2as. This equation relates final velocity, initial velocity, acceleration and displacement without involving time. For example, if a question gives you initial velocity, acceleration and distance, and asks for final velocity, this is the correct formula to apply. Remember it connects the two velocities with displacement and acceleration only.

What is the difference between speed and velocity?+

Speed is the rate of change of distance, a scalar quantity with only magnitude (like 20 m/s). Velocity is the rate of change of displacement, a vector quantity with both magnitude and direction (like 20 m/s north). An object moving in a circle at constant speed has changing velocity because its direction continuously changes, even though speed remains constant. This is a common conceptual question in CBSE exams.

How do I calculate average speed when the motion has multiple segments or rest periods?+

Average speed is always total distance divided by total time. Add up the distances of all segments to get total distance. Add up the time intervals of all segments, including any rest or stop time, to get total time. Then divide total distance by total time. Do not take the arithmetic average of individual speeds unless the time intervals are exactly equal, which is rarely the case in exam questions.

What does negative acceleration mean? Is it different from retardation?+

Negative acceleration means the acceleration is in the direction opposite to the positive direction you have chosen. If you choose the direction of motion as positive and the object is slowing down, its acceleration is negative. This is also called retardation or deceleration. For example, if a car moving east at 30 m/s brakes with acceleration -5 m/s², it is slowing down by 5 m/s every second until it stops.

Can displacement be zero even if distance is not zero?+

Yes, absolutely. If an object moves and returns to its starting point, displacement is zero (because start and end positions are the same), but distance is the total path length covered, which is not zero. For example, running one full lap around a 400 m track gives distance 400 m but displacement 0 m. This is a key difference between the two quantities and a common exam question.

Do the three equations of motion apply to all types of motion?+

No, the three equations of motion (v = u + at, s = ut + ½at², v² = u² + 2as) apply only to uniformly accelerated motion, meaning motion with constant acceleration. They do not apply to non-uniform acceleration or to circular motion where acceleration direction changes. For problems involving variable acceleration, these formulas cannot be used and other methods like calculus or graphical analysis are needed (covered in higher classes).

Why is motion called relative? Can you give a simple example?+

Motion is relative because whether an object is moving or at rest depends on the observer or reference point. A passenger sitting in a moving train is at rest relative to the train (they do not change position inside the train), but in motion relative to trees and buildings outside. Similarly, the Moon is in motion relative to Earth, but at rest relative to a spacecraft orbiting at the same speed. Always specify the reference frame when describing motion.

What are the SI units of distance, speed, velocity and acceleration that I must use in exams?+

Distance and displacement: meter (m). Time: second (s). Speed and velocity: meter per second (m/s). Acceleration: meter per second squared (m/s²). These are the SI units you must use in calculations unless the question specifically asks for km, km/h or other units. Always convert given data to SI units before substituting into formulas, then convert the final answer to the unit asked for in the question, if different.

Related resources

Important Questions: CBSE Class 9 Physics Chapter 7 Motion CBSE Class 9 Physics Chapter 7 Motion Worksheet with Answers NCERT Solutions for CBSE Class 9 Physics Chapter 7: Motion CBSE Class 9 Physics Chapter 7 Motion — Notes CBSE Class 9 Mathematics Chapter 1 Number Systems — Notes CBSE Class 9 Mathematics — Number Systems: complete chapter guide Class 9 Physics Chapter 7: Motion – Complete Notes, Definitions & Examples Class 9 Mathematics Chapter 2 Polynomials — Formulas & Key Points

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