1. Describing Motion
- Definition: Motion is a change in an object’s position with time (e.g., birds flying, cars moving).
- Rest vs. Motion:
- Rest: Object’s position doesn’t change (e.g., classroom walls, Activity 7.1).
- Motion: Position changes (e.g., blood flow, planetary motion).
- Indirect Evidence: Motion inferred from effects (e.g., air movement seen via dust or leaves).
- Relative Motion:
- Motion depends on the observer’s frame (e.g., trees appear to move backward for bus passengers, but the bus moves for roadside observers).
- Activity 7.2: Train at rest may appear moving due to nearby train’s motion.
- Types of Motion: Straight line, circular, rotational, vibrational, or combinations.
- Reference Point (Origin):
- Position described relative to a fixed point (e.g., school 2 km north of railway station).
- Choice of reference point is flexible.
- Motion Along a Straight Line:
- Example (Fig. 7.1): Object moves from O to A (60 km), back to C via B (35 km).
- Distance: Total path length (O to A + A to C = 95 km); scalar, only magnitude.
- Displacement: Shortest distance from initial to final position (O to C = 25 km); vector, includes direction.
- Case: Distance = displacement when motion is in one direction (O to A = 60 km).
- Activity 7.3: Walk along basketball court sides; distance is total path, displacement is straight-line distance between start and end.
- Activity 7.4: Car odometer shows 1850 km (distance); displacement requires road map for shortest path.
- Uniform vs. Non-Uniform Motion:
- Uniform Motion: Equal distances in equal time intervals (e.g., 5 m every second).
- Non-Uniform Motion: Unequal distances in equal time intervals (e.g., car in traffic).
- Activity 7.5 (Table 7.1):
- Object A: Uniform (10 m every 15 min).
- Object B: Non-uniform (varying distances, e.g., 12 m, 7 m, 4 m).
- Questions:
- Zero Displacement: Possible if object returns to start (e.g., Usha swims pool and back, displacement = 0).
- Farmer Example: Square field (10 m side), 40 s per round. At 2 min 20 s (140 s), completes 3.5 rounds (displacement = 10 m diagonally).
- Displacement Facts: Can be zero; magnitude is never greater than distance.
Activity: Walk a square path and measure distance vs. displacement!
2. Measuring Rate of Motion
- Speed:
- Definition: Distance travelled per unit time; scalar, only magnitude.
- SI Unit: m/s (also cm/s, km/h).
- Formula: \( v = \frac{s}{t} \) (s = distance, t = time).
- Average Speed: Total distance ÷ total time for non-uniform motion.
- Example 7.1: Object travels 16 m in 4 s, then 16 m in 2 s. Average speed = 32 m ÷ 6 s = 5.33 m/s.
- Velocity:
- Definition: Speed with direction; vector.
- Can be uniform or variable (changes in speed, direction, or both).
- Average Velocity: For uniform acceleration, \( v_{av} = \frac{u + v}{2} \) (u = initial velocity, v = final velocity).
- Example 7.3: Usha swims 180 m in 1 min (pool and back). Average speed = 3 m/s; average velocity = 0 m/s (displacement = 0).
- Examples:
- Example 7.2: Car odometer from 2000 km to 2400 km in 8 h. Average speed = 400 km ÷ 8 h = 50 km/h = 13.9 m/s.
- Activities:
- Activity 7.6: Walk to school at 4 km/h, measure time to estimate distance.
- Activity 7.7: Time thunder after lightning; calculate distance using speed of sound (346 m/s).
- Questions:
- Speed vs. Velocity: Speed is scalar (magnitude only); velocity is vector (magnitude + direction).
- Average Velocity = Average Speed: When motion is in one direction (no return).
- Odometer: Measures distance travelled.
- Uniform Motion Path: Straight line in distance-time graph.
- Spaceship Signal: 5 min at 3×10⁸ m/s = 9×10¹⁰ m.
Fun Fact: Velocity tells you where an object is headed, not just how fast!
3. Rate of Change of Velocity
- Acceleration:
- Definition: Change in velocity per unit time; vector.
- Formula: \( a = \frac{v - u}{t} \) (v = final velocity, u = initial velocity, t = time).
- SI Unit: m/s².
- Sign: Positive if in direction of velocity; negative if opposite (deceleration).
- Types:
- Uniform Acceleration: Velocity changes by equal amounts in equal time intervals (e.g., freely falling body).
- Non-Uniform Acceleration: Velocity changes unequally (e.g., car in traffic).
- Examples:
- Example 7.4: Bicycle from rest to 6 m/s in 30 s (a = 0.2 m/s²); brakes to 4 m/s in 5 s (a = -0.4 m/s²).
- Activity 7.8:
- Identify motions:
- Acceleration with motion: Car speeding up.
- Acceleration against motion: Car braking.
- Uniform acceleration: Falling object.
- Non-uniform acceleration: Car in traffic.
- Identify motions:
- Questions:
- Uniform Acceleration: Equal velocity changes in equal times.
- Non-Uniform Acceleration: Unequal velocity changes.
- Bus: 80 km/h to 60 km/h in 5 s; a = -1.11 m/s².
- Train: Rest to 40 km/h in 10 min; a = 0.0185 m/s².
Activity: Time a car speeding up or slowing down!
4. Graphical Representation of Motion
- Distance-Time Graphs:
- Setup: Time (x-axis), distance (y-axis).
- Uniform Motion: Straight line (Fig. 7.3); distance proportional to time.
- Speed Calculation: \( v = \frac{s_2 - s_1}{t_2 - t_1} \) (slope of graph).
- Non-Uniform Motion: Curved line (Fig. 7.4, Table 7.2: car distances 0, 1, 4, 9, 16, 25, 36 m).
- Activity 7.9: Train (Table 7.4) distance-time graph shows uniform motion between stations.
- Activity 7.10: Feroz and Sania’s bicycle motion (Table 7.5); Feroz faster (steeper slope).
- Velocity-Time Graphs:
- Setup: Time (x-axis), velocity (y-axis).
- Uniform Velocity: Horizontal line (Fig. 7.5, 40 km/h).
- Distance: Area under graph (rectangle for uniform velocity).
- Uniform Acceleration: Straight line (Fig. 7.6, Table 7.3: car velocities 0, 9, 18, 27, 36, 45, 54 km/h).
- Distance: Area under graph (rectangle + triangle for acceleration).
- Non-Uniform Acceleration: Curved lines (Fig. 7.7a: decreasing velocity; 7.7b: varying velocity).
- Questions:
- Distance-Time Graphs: Straight for uniform, curved for non-uniform.
- Horizontal Distance-Time: Object at rest.
- Horizontal Speed-Time: Uniform motion.
- Velocity-Time Graph Area: Measures displacement.
Activity: Plot a distance-time graph for your walk to school!
5. Equations of Motion
- Applicability: For uniform acceleration in a straight line.
- Equations:
- \( v = u + at \) (velocity-time relation).
- \( s = ut + \frac{1}{2}at^2 \) (position-time relation).
- \( 2as = v^2 - u^2 \) (position-velocity relation).
- Variables: u = initial velocity, v = final velocity, a = acceleration, t = time, s = distance.
- Examples:
- Example 7.5: Train from rest to 72 km/h (20 m/s) in 5 min (300 s). Acceleration = 1/15 m/s², distance = 3 km.
- Example 7.6: Car from 18 km/h (5 m/s) to 36 km/h (10 m/s) in 5 s. Acceleration = 1 m/s², distance = 37.5 m.
- Example 7.7: Car brakes at -6 m/s², stops in 2 s. Initial velocity = 12 m/s, distance = 12 m.
- Questions:
- Bus: 0.1 m/s² for 2 min; speed = 12 m/s, distance = 720 m.
- Train: 90 km/h, -0.5 m/s²; distance = 625 m.
- Trolley: 2 cm/s², 3 s; velocity = 6 cm/s.
- Car: 4 m/s², 10 s; distance = 200 m.
- Stone: 5 m/s up, -10 m/s²; height = 1.25 m, time = 0.5 s.
Activity: Solve a motion problem using equations!
6. Uniform Circular Motion
- Definition: Motion in a circular path with constant speed; accelerated due to direction change.
- Examples: Moon, Earth, satellites, cyclist on circular track.
- Characteristics:
- Constant speed, but velocity changes due to direction.
- Speed: \( v = \frac{2\pi r}{t} \) (r = radius, t = time for one revolution).
- Activity 7.7:
- Tie stone to thread, spin in circle, release; stone moves tangentially (straight line).
- Shows direction changes continuously in circular motion.
- Track Shapes (Fig. 7.8):
- Rectangular: 4 direction changes.
- Hexagonal: 6 changes.
- Octagonal: 8 changes.
- Circular: Continuous direction change as sides increase.
- Questions:
- Athlete: 200 m diameter track, 40 s per round; at 140 s, distance = 1750 m, displacement = 141.4 m.
- Satellite: 42250 km orbit, 24 h; speed = 11065.6 km/h.
Activity: Spin a stone on a thread and release it!
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