Motion and Time — Measuring Movement
"'An object is in MOTION if its position CHANGES with time. The study of motion is the FOUNDATION of physics.'"
1. What Is Motion?
Motion: A change in the POSITION of an object with respect to TIME and a REFERENCE POINT (frame of reference).
Rest: An object is AT REST if its position does NOT change with respect to the reference point.
'Everything in the universe is in MOTION relative to something. A book on a table appears at rest — but it is moving with the Earth as it rotates and revolves!'
Types of Motion
| Type | Description | Examples |
|---|---|---|
| Rectilinear (straight line) | Motion along a STRAIGHT line | A car on a straight road, a falling apple |
| Circular | Motion along a CIRCULAR path | A merry-go-round, earth around the sun |
| Periodic | Motion that REPEATS after a fixed time interval | Pendulum, Earth's rotation, heartbeat |
| Oscillatory | Back-and-forth motion about a mean position | Swing, pendulum, vibrating string |
| Rotational | Object spins about an axis | Fan blades, bicycle wheel |
2. Speed — How Fast or Slow
Speed: The DISTANCE covered by an object in a UNIT of TIME.
Formula: Speed = Distance / Time or v = s/t
Units:
- SI unit: metre per second (m/s)
- Common unit: kilometre per hour (km/h)
Conversion: 'To convert km/h to m/s: MULTIPLY by 5/18. To convert m/s to km/h: MULTIPLY by 18/5.'
| Speed | In km/h | In m/s |
|---|---|---|
| Walking | 5 km/h | 1.39 m/s |
| Running | 15 km/h | 4.17 m/s |
| Bicycle | 15-20 km/h | 4.17-5.56 m/s |
| Car (city) | 40-60 km/h | 11.1-16.7 m/s |
| Express train | 120 km/h | 33.3 m/s |
| Aeroplane | 800 km/h | 222 m/s |
| Sound | 1224 km/h | 340 m/s |
| Light | 1,080,000,000 km/h | 300,000,000 m/s |
Uniform vs Non-Uniform Motion
| Aspect | Uniform Motion | Non-Uniform Motion |
|---|---|---|
| Speed | CONSTANT (does not change) | VARIABLE (changes with time) |
| Distance-time graph | STRAIGHT LINE | CURVED line |
| Examples | Car on cruise control on highway | Bus in city traffic, a ball thrown in air |
Worked Example 1: 'A train travels 240 km in 4 hours. Find its speed.' Speed = 240/4 = 60 km/h. In m/s: 60 × (5/18) = 16.67 m/s.
Worked Example 2: 'Sound travels at 340 m/s. How far does it travel in 5 seconds?' Distance = Speed × Time = 340 × 5 = 1700 m = 1.7 km.
Worked Example 3: 'How long will a bus travelling at 40 km/h take to cover 160 km?' Time = Distance / Speed = 160/40 = 4 hours.
3. Measurement of Time
Ancient Methods
| Method | How It Worked |
|---|---|
| Sundial | Shadow of a stick changes position with the Sun's movement |
| Hourglass | Sand flows from one bulb to another at a constant rate |
| Water clock | Water drips at a constant rate from one container to another |
| Candle clock | Markings on a candle — time is read by how much has melted |
Modern Time Measurement
| Device | Accuracy | Use |
|---|---|---|
| Quartz watch | Very accurate | Daily use |
| Atomic clock | EXTREMELY accurate (loses 1 second in millions of years) | GPS, internet, scientific research |
Units of Time
| Unit | Equivalence |
|---|---|
| 1 minute | 60 seconds |
| 1 hour | 60 minutes = 3600 seconds |
| 1 day | 24 hours |
| 1 year | 365 days |
| 1 decade | 10 years |
| 1 century | 100 years |
4. The Simple Pendulum
Pendulum: A small bob (weight) suspended from a fixed point by a light, inextensible string.
Parts of a Pendulum
| Part | Description |
|---|---|
| Bob | The weight at the end |
| String/Thread | Connects bob to support |
| Point of suspension | Fixed point from which the pendulum hangs |
| Mean position | Centre position where the bob hangs vertically |
| Amplitude | Maximum displacement from the mean position |
Periodic Motion of a Pendulum
'A pendulum swings back and forth — this is an OSCILLATORY motion. Its period DEPENDS on the length of the string, NOT on the mass of the bob or the amplitude (for small swings).'
One oscillation: One COMPLETE to-and-fro motion (from one extreme to the other and back).
Time period (T): Time taken for ONE complete oscillation.
Frequency (f): Number of oscillations per SECOND. f = 1/T.
Factors affecting the time period:
- Length of string: LONGER string → SLOWER (LARGER time period). This is the ONLY factor that matters for small angles.
- Mass of bob: Does NOT affect the time period.
- Amplitude: For small swings, does NOT affect the time period.
Worked Example: 'A pendulum takes 20 seconds to complete 10 oscillations. Find its time period.' T = Total time / Number of oscillations = 20/10 = 2 seconds.
Uses of Pendulums
- Pendulum CLOCKS (time measurement)
- Metronome for MUSIC
- Measuring GRAVITY (g)
5. Distance-Time Graphs
Graph: A VISUAL representation of how distance changes with time.
| Type of Motion | Graph Shape | What It Means |
|---|---|---|
| Object at rest | HORIZONTAL line (parallel to time axis) | Distance does NOT change |
| Uniform motion | STRAIGHT LINE through origin | Constant speed |
| Non-uniform motion | CURVED line | Speed is changing |
| Faster uniform motion | STEEPER straight line | Higher speed |
'The SLOPE of a distance-time graph tells you the SPEED. A steeper slope = FASTER speed.'
Reading a Graph
'If a car travels 100 km in 2 hours, the distance-time graph is a straight line from (0,0) to (2,100). The slope = 100/2 = 50 km/h.'
6. Common Mistakes and Fixes
| Mistake | Why It Is Wrong | Correct Approach |
|---|---|---|
| Speed = Time/Distance | Wrong formula. Speed = DISTANCE/TIME | Speed = Distance ÷ Time |
| km/h to m/s = × 18/5 | Wrong conversion factor | km/h → m/s = × 5/18 (not 18/5) |
| A heavier pendulum swings faster | Mass does NOT affect the time period | Only LENGTH affects the pendulum's period |
| Uniform circular motion has constant velocity | DIRECTION changes, so VELOCITY changes even if SPEED is constant | Circular motion is ACCELERATED motion |
| All motions with repeating pattern are periodic | Repeating pattern but NOT about a mean position | Periodic motion = repeats at REGULAR time intervals |
7. AP SSC Exam Focus
| Topic | Marks | Question Type |
|---|---|---|
| Speed — distance and time | 3-4 | Word problems |
| Uniform vs non-uniform motion | 2-3 | Distinguish, examples |
| Simple pendulum — time period | 3-4 | Calculation, factors |
| Distance-time graphs | 2-3 | Interpretation |
| Units of time and speed conversion | 2-3 | Conversion problems |
Quick Self-Test
Q1. A car travels 180 km in 3 hours. Find its speed in km/h and m/s. A1. Speed = 180/3 = 60 km/h. In m/s: 60 × (5/18) = 16.67 m/s.
Q2. Distinguish between uniform and non-uniform motion. A2. Uniform motion: constant speed, equal distances in equal time intervals. Non-uniform motion: changing speed, unequal distances in equal time intervals.
Q3. A pendulum completes 15 oscillations in 30 seconds. Find its time period. A3. T = 30/15 = 2 seconds.
Q4. What does the slope of a distance-time graph represent? A4. The slope represents SPEED. A steeper slope means faster speed.
Q5. How does the length of a pendulum affect its time period? A5. A LONGER pendulum has a LARGER time period (swings slower). The time period is proportional to the square root of the length.
Q6. Convert 90 km/h to m/s. A6. 90 × (5/18) = 25 m/s.
Q7. Why is circular motion considered accelerated motion even if speed is constant? A7. Because DIRECTION changes continuously. Acceleration = change in velocity (speed OR direction). Since direction changes, velocity changes, so there IS acceleration.
