Motion — Study Notes for SOF NSO

Overview

Motion is a foundational topic in physics that appears in virtually every competitive science exam, including NSO Class 9 and 10. Understanding motion means describing *how* objects move — their position changes over time — using quantities like distance, displacement, speed, velocity, and acceleration. This topic builds the language of kinematics, which is essential for later chapters like Force, Gravitation, and Work & Energy.

In NSO, expect **3–5 direct questions** from this topic: numerical problems using equations of motion, conceptual questions distinguishing scalar vs vector quantities, and graph-based problems (distance-time, velocity-time). Mastery here means being able to set up equations quickly, interpret motion graphs correctly, and avoid sign-convention errors. Students often lose marks by confusing distance with displacement or misapplying equations when acceleration isn't uniform — so clarity on definitions and assumptions is critical.

The chapter revolves around **uniformly accelerated motion in a straight line**, which means constant acceleration. Real NSO problems test your ability to apply three kinematic equations and read graphical data under time pressure.

Key Concepts

• **Distance vs Displacement**: Distance is the total path length traveled (scalar, always positive). Displacement is the shortest straight-line distance from start to finish with direction (vector, can be zero or negative).
• **Speed vs Velocity**: Speed is distance/time (scalar). Velocity is displacement/time (vector). Average velocity can be zero even if average speed is not, if the object returns to its starting point.
• **Acceleration**: Rate of change of velocity. Positive acceleration means speeding up in the positive direction or slowing down in the negative direction. Negative acceleration (retardation) means slowing down in the positive direction.
• **Uniform Motion**: Object covers equal distances in equal intervals of time — velocity is constant, acceleration is zero.
• **Non-Uniform Motion**: Velocity changes with time — acceleration is non-zero. The three kinematic equations apply only when acceleration is constant.
• **Scalar vs Vector**: Distance and speed are scalars (magnitude only). Displacement, velocity, and acceleration are vectors (magnitude and direction). NSO often tests whether you recognize the vector nature in problems.
• **Instantaneous vs Average**: Instantaneous velocity is velocity at a specific instant. Average velocity is total displacement divided by total time. For uniform acceleration, average velocity = (initial + final velocity)/2.
• **Graphical Representation**: Distance-time graph slope gives speed. Velocity-time graph slope gives acceleration, and the area under the curve gives displacement. These graph problems are NSO favorites.

Formulas / Key Facts

1. **Average Speed** = Total distance / Total time 2. **Average Velocity** = Total displacement / Total time 3. **Acceleration** = (Final velocity − Initial velocity) / Time = (v − u) / t 4. **First Equation of Motion**: v = u + at (final velocity in terms of initial velocity, acceleration, time) 5. **Second Equation of Motion**: s = ut + ½at² (displacement in terms of initial velocity, acceleration, time) 6. **Third Equation of Motion**: v² = u² + 2as (relates velocity, acceleration, displacement without time) 7. **Displacement in nth second**: sₙₜₕ = u + a(n − ½) (distance covered in the nth second only) 8. **SI Units**: Distance/displacement in meters (m), speed/velocity in m/s, acceleration in m/s². 9. **Uniform motion**: a = 0, so v = u (constant velocity) and s = vt. 10. **Free fall**: Special case with a = g = 9.8 m/s² downward (covered in Gravitation, but motion equations apply).

Worked Examples

**Example 1: Basic equation application** A car starts from rest and accelerates uniformly at 2 m/s² for 5 seconds. Find (i) final velocity, (ii) distance covered.

*Solution:* Given u = 0, a = 2 m/s², t = 5 s. (i) v = u + at = 0 + 2×5 = 10 m/s (ii) s = ut + ½at² = 0 + ½×2×5² = 25 m

**Example 2: Third equation when time is not given** A train moving at 20 m/s is brought to rest in 100 m by applying brakes. Find the retardation.

*Solution:* Given u = 20 m/s, v = 0 (comes to rest), s = 100 m. Use v² = u² + 2as 0 = 400 + 2×a×100 200a = −400 a = −2 m/s² (negative sign indicates retardation)

**Example 3: Average velocity vs average speed** A person walks 4 km east in 1 hour, then 3 km west in the next hour. Find average speed and average velocity.

*Solution:* Total distance = 4 + 3 = 7 km, total time = 2 h. Average speed = 7/2 = 3.5 km/h Net displacement = 4 − 3 = 1 km east, total time = 2 h. Average velocity = 1/2 = 0.5 km/h east

**Example 4: Graph interpretation** A velocity-time graph shows a straight line from (0,10) to (5,30) in m/s and seconds. Find acceleration and displacement.

*Solution:* Slope = acceleration = (30−10)/(5−0) = 20/5 = 4 m/s² Displacement = area under graph = area of trapezium = ½×(10+30)×5 = 100 m

Common Mistakes

• **Confusing distance with displacement**: Using total path length instead of net change in position. **Fix**: Always check if the question asks for distance (scalar) or displacement (vector). If an object returns to start, displacement = 0 but distance ≠ 0.
• **Wrong sign for acceleration**: Treating retardation (deceleration) as positive when velocity decreases. **Fix**: If velocity decreases in the positive direction, acceleration is negative. Set a consistent direction as positive at the start.
• **Misapplying equations when acceleration isn't constant**: Using v = u + at for motion with varying acceleration. **Fix**: The three equations of motion apply *only* to uniformly accelerated motion. Check the problem statement.
• **Forgetting units**: Mixing km/h with m/s or not converting time to seconds. **Fix**: Convert all quantities to SI units (m, s, m/s, m/s²) before plugging into formulas.
• **Calculating average velocity as (distance)/(time)**: Using distance instead of displacement for average velocity. **Fix**: Average velocity = displacement/time. For round trips or back-and-forth motion, displacement can be zero, making average velocity zero.

Quick Reference

• **Scalar quantities in motion**: Distance, speed. **Vector quantities**: Displacement, velocity, acceleration.
• **v = u + at** for final velocity. **s = ut + ½at²** for displacement. **v² = u² + 2as** when time is unknown.
• **Distance-time graph**: Slope = speed. Horizontal line = rest. Curved line = non-uniform motion.
• **Velocity-time graph**: Slope = acceleration. Area under curve = displacement. Horizontal line = uniform velocity.
• **Retardation**: Negative acceleration — object slowing down. Common in braking/stopping problems.
• **Average velocity can be zero** even if average speed is not — happens when net displacement is zero (round trip).