9th Class Physics Chapter 2 Notes PDF — Kinematics

<p><em>Parhai — Free Punjab Board Notes</em></p> <h2>Key Concepts</h2> <h3>Rest and Motion</h3> <p>A body is <strong>at rest</strong> when its position stays fixed relative to the objects around it. A body is <strong>in motion</strong> when its position keeps changing with respect to its surroundings. The branch of physics that describes motion without asking which forces cause it is called <strong>kinematics</strong>.</p> <h3>The Three Types of Motion</h3> <p><strong>1. Translatory motion</strong> — the body travels along a path without spinning on its own axis. The path may be straight or curved. It has three sub-types:</p> <ul> <li><strong>Linear motion:</strong> travel along a straight line, for example a stone falling vertically or an aeroplane flying straight ahead.</li> <li><strong>Circular motion:</strong> travel along a circular path, for example the Earth revolving around the Sun, the Moon circling the Earth, or a toy train running on a circular track.</li> <li><strong>Random motion:</strong> irregular, unpredictable movement, for example insects flying about or dust particles drifting in the air.</li> </ul> <p><strong>2. Rotatory motion</strong> — the body spins about its own axis, for example a wheel turning on its axle, a steering wheel being turned, or the Earth rotating to produce day and night.</p> <p><strong>3. Vibratory motion</strong> — the body swings to and fro about a fixed central position, for example a baby rocking in a cradle, the hammer of a ringing electric bell, or the plucked string of a sitar.</p> <p><em>Interesting case:</em> riders in a Ferris wheel travel in a circle but never spin themselves, so their motion is translatory (circular) — not rotatory.</p> <h3>Scalars and Vectors</h3> <p><strong>Scalar</strong> quantities are fully described by their magnitude alone: mass, length, time, speed, distance, volume, work and energy.</p> <p><strong>Vector</strong> quantities need both magnitude and direction: displacement, velocity, acceleration, force, momentum and torque.</p> <p>On paper, a vector is drawn as a straight line with an arrowhead. The length of the line (on a chosen scale) shows the magnitude, and the arrowhead points in the direction of the quantity. Because direction is part of a vector, vectors cannot be added or subtracted like ordinary numbers.</p> <h3>Distance and Displacement</h3> <p><strong>Distance</strong> is the total length of the path actually travelled — a scalar. <strong>Displacement</strong> is the shortest straight-line distance between the starting and finishing points, taken together with its direction — a vector.</p> <h3>Speed and Velocity</h3> <ul> <li><strong>Speed</strong> = distance covered ÷ time taken. It is a scalar with unit m/s.</li> <li><strong>Velocity</strong> = displacement ÷ time taken. It is a vector with unit m/s.</li> </ul> <p>A body moving at a constant speed can still be accelerating if its direction keeps changing — for instance, a car driving at steady speed around a roundabout.</p> <h3>Acceleration</h3> <p><strong>Acceleration</strong> is the rate of change of velocity: a = (vf − vi) ÷ t, measured in m/s².</p> <ul> <li><strong>Uniform acceleration:</strong> the velocity grows by equal amounts in every equal interval of time.</li> <li><strong>Positive acceleration:</strong> the velocity is increasing with time.</li> <li><strong>Negative acceleration (deceleration or retardation):</strong> the velocity is decreasing. A car heading east can have westward acceleration while its speed is falling.</li> <li>A body cruising with perfectly uniform velocity has zero acceleration, because there is no change in velocity at all.</li> </ul> <h3>Reading Motion Graphs</h3> <p><strong>Speed–time graph:</strong></p> <ul> <li>The <strong>slope</strong> of the line gives the acceleration. A straight, tilted line means uniform acceleration.</li> <li>The <strong>area</strong> under the line gives the distance covered.</li> <li>One such graph reveals the initial speed, the final speed, the distance covered in time t, and the acceleration.</li> <li>A horizontal line means constant speed (no acceleration); a curved line means the speed is changing unevenly.</li> </ul> <p><strong>Distance–time graph:</strong></p> <ul> <li>The <strong>slope</strong> of the line gives the speed.</li> <li>A straight line tilted to the time axis means constant speed.</li> <li>A line running parallel to the time axis means the body is at rest.</li> <li>A curved line means the speed is variable.</li> </ul> <p>In general, the slope (gradient) of any graph is the change along the vertical axis divided by the change along the horizontal axis.</p> <h3>Equations of Motion</h3> <p>For a body moving in a straight line with uniform acceleration <em>a</em>, starting with velocity <em>vi</em> and reaching <em>vf</em> after time <em>t</em> while covering distance <em>S</em>:</p> <table> <tr><th>Equation</th><th>Tells you</th></tr> <tr><td>vf = vi + at</td><td>final velocity</td></tr> <tr><td>S = vit + ½at²</td><td>distance covered</td></tr> <tr><td>2aS = vf² − vi²</td><td>velocity–distance relation (no time)</td></tr> </table> <p>These come straight from the speed–time graph: the first from the slope of the line, the second from the area beneath it (a rectangle plus a triangle), and the third by combining the two.</p> <h3>Gravitational Acceleration</h3> <p>Objects falling freely speed up at the <strong>gravitational acceleration g</strong>, which is 10 m/s² at the Earth's surface (the value used in the Punjab Board syllabus). Take g as positive when the body moves downward and negative when it moves upward. A ball tossed straight up momentarily has zero velocity at the very top of its flight.</p> <h2>Questions & Answers</h2> <h3>Q1. What are rest and motion?</h3> <p><strong>Rest:</strong> the body does not change its position relative to its surroundings.<br><strong>Motion:</strong> the body continuously changes its position relative to its surroundings.</p> <h3>Q2. Name and describe the three types of motion with one example each.</h3> <p><strong>Translatory</strong> — movement along a path without spinning (a car driving straight). <strong>Rotatory</strong> — spinning about the body's own axis (a spinning wheel). <strong>Vibratory</strong> — to-and-fro movement about a fixed point (a swinging pendulum).</p> <h3>Q3. What is translatory motion? List its types.</h3> <p>When a body moves along a line without any rotation, its motion is translatory. Its three types are <strong>linear</strong> (straight-line, e.g. a falling object), <strong>circular</strong> (round path, e.g. the Moon around the Earth) and <strong>random</strong> (irregular, e.g. flying insects).</p> <h3>Q4. How is circular motion different from rotatory motion?</h3> <p>In <strong>circular motion</strong> the whole body travels around a circular path (Earth orbiting the Sun). In <strong>rotatory motion</strong> the body spins about an axis passing through itself (the Earth spinning to cause day and night).</p> <h3>Q5. Distinguish between distance and displacement.</h3> <p><strong>Distance</strong> is the full length of the travelled path and is a scalar. <strong>Displacement</strong> is the shortest distance between the start and end points, with direction, and is a vector.</p> <h3>Q6. Distinguish between speed and velocity.</h3> <p><strong>Speed</strong> is distance covered per unit time — a scalar. <strong>Velocity</strong> is displacement per unit time — a vector, because direction is included.</p> <h3>Q7. What are scalars and vectors? Give examples.</h3> <p><strong>Scalars</strong> need only magnitude: mass, length, time, speed, volume, work, energy. <strong>Vectors</strong> need magnitude plus direction: displacement, velocity, acceleration, force, momentum, torque. A vector is drawn as an arrowed line whose length shows size and whose arrow shows direction; vectors cannot be combined like plain numbers because their directions matter.</p> <h3>Q8. Define acceleration. When is it uniform, positive or negative?</h3> <p>Acceleration is the rate of change of velocity. It is <strong>uniform</strong> when velocity changes by equal amounts in equal times; <strong>positive</strong> when velocity increases; <strong>negative</strong> (deceleration) when velocity decreases.</p> <h3>Q9. A body moves with uniform velocity. What is its acceleration?</h3> <p>Zero. Acceleration measures the change in velocity, and a uniform velocity never changes, so the acceleration is zero.</p> <h3>Q10. Can a body moving east have acceleration toward the west?</h3> <p>Yes. If the eastward-moving body is slowing down, its acceleration points opposite to its velocity — toward the west. That is deceleration.</p> <h3>Q11. What information does a speed–time graph give?</h3> <p>Its slope gives the acceleration, and the area under it gives the distance covered. From it you can read the initial speed, the final speed, the distance covered in a given time, and the acceleration. A straight tilted line means uniform acceleration; a horizontal line means constant speed.</p> <h3>Q12. How do you interpret a distance–time graph?</h3> <p>The slope gives the speed. A tilted straight line means constant speed, a horizontal line means the body is at rest, and a curved line means the speed is changing.</p> <h3>Q13. What is gravitational acceleration and what is its value?</h3> <p>It is the acceleration of freely falling bodies, denoted g, equal to 10 m/s² at the Earth's surface. It counts as positive for downward motion and negative for upward motion.</p> <h3>Q14. Write the three equations of motion.</h3> <p>vf = vi + at; S = vit + ½at²; 2aS = vf² − vi².</p> <h3>Q15. Why do Ferris-wheel riders have translatory motion but not rotatory motion?</h3> <p>Their seats travel around a circle without the riders spinning on their own axes, so the motion is circular translatory motion — there is no rotation of the body itself.</p> <h3>Solved Numerical 1</h3> <p><strong>Question:</strong> A train moves with a uniform velocity of 36 km/h for 10 s. Find the distance travelled.<br> <strong>Solution:</strong> Convert: 36 km/h = 36 × 1000 ÷ 3600 = 10 m/s. Distance S = v × t = 10 × 10 = <strong>100 m</strong>.</p> <h3>Solved Numerical 2</h3> <p><strong>Question:</strong> A car starts from rest and reaches 25 m/s in 20 s. Find the distance covered.<br> <strong>Solution:</strong> Acceleration a = (25 − 0) ÷ 20 = 1.25 m/s². Distance S = vit + ½at² = 0 + ½ × 1.25 × 400 = <strong>250 m</strong>.</p> <h3>Solved Numerical 3</h3> <p><strong>Question:</strong> A tennis ball is hit straight up at 30 m/s and takes 3 s to reach the top. Find the maximum height and the total time to return to the ground.<br> <strong>Solution:</strong> Take g = −10 m/s² upward. Height h = vit + ½gt² = 30 × 3 − 5 × 9 = 90 − 45 = <strong>45 m</strong>. The ball takes the same 3 s to fall back, so total time = <strong>6 s</strong>.</p> <h3>Solved Numerical 4</h3> <p><strong>Question:</strong> A train's speed falls from 96 km/h to 48 km/h over 800 m with constant retardation. How much farther will it travel before stopping?<br> <strong>Solution:</strong> vi = 96 km/h = 26.67 m/s, vf = 48 km/h = 13.33 m/s. From 2aS = vf² − vi²: a = (177.78 − 711.11) ÷ 1600 = −0.333 m/s². Now with vi = 13.33 m/s and vf = 0: S = (0 − 177.78) ÷ (2 × −0.333) = <strong>266.67 m</strong>.</p> <h2>MCQs — Test Yourself</h2> <ol> <li>A body has translatory motion when it moves along a:<br>(a) straight line <strong>✓</strong> (b) fixed axis (c) mean position (d) spiral</li> <li>The motion of a body about its own axis is called:<br>(a) circular motion (b) <strong>rotatory motion ✓</strong> (c) vibratory motion (d) random motion</li> <li>Which of the following is a vector quantity?<br>(a) speed (b) distance (c) <strong>displacement ✓</strong> (d) time</li> <li>If an object moves with constant speed, its distance–time graph is a straight line:<br>(a) along the time axis (b) along the distance axis (c) parallel to the time axis (d) <strong>inclined to the time axis ✓</strong></li> <li>A straight line parallel to the time axis on a distance–time graph means the object is:<br>(a) moving with constant speed (b) <strong>at rest ✓</strong> (c) moving with variable speed (d) accelerating</li> <li>A car's speed–time graph shows its speed rising from 3 m/s to 9 m/s in 4 seconds. Its acceleration is:<br>(a) <strong>1.5 m/s² ✓</strong> (b) 3 m/s² (c) 6 m/s² (d) 12 m/s²</li> <li>Uniform acceleration is shown by a speed–time graph that is:<br>(a) a curve (b) a horizontal line (c) <strong>a straight inclined line ✓</strong> (d) a zigzag</li> <li>Dividing the displacement of a moving body by time gives:<br>(a) speed (b) acceleration (c) <strong>velocity ✓</strong> (d) distance</li> <li>A ball is thrown vertically upward. Its velocity at the highest point is:<br>(a) −10 m/s (b) <strong>zero ✓</strong> (c) 10 m/s (d) maximum</li> <li>A change in position is called:<br>(a) speed (b) velocity (c) <strong>displacement ✓</strong> (d) distance</li> <li>A train moves at 36 km/h. Its speed in m/s is:<br>(a) <strong>10 m/s ✓</strong> (b) 20 m/s (c) 25 m/s (d) 30 m/s</li> <li>A car starts from rest and gains 25 m/s in 20 s. The distance covered is:<br>(a) 31.25 m (b) <strong>250 m ✓</strong> (c) 500 m (d) 5000 m</li> </ol> <h2>Key Formulas</h2> <table> <tr><th>Quantity</th><th>Formula</th></tr> <tr><td>Speed</td><td>v = distance ÷ time</td></tr> <tr><td>Velocity</td><td>v = displacement ÷ time</td></tr> <tr><td>Acceleration</td><td>a = (vf − vi) ÷ t</td></tr> <tr><td>1st equation of motion</td><td>vf = vi + at</td></tr> <tr><td>2nd equation of motion</td><td>S = vit + ½at²</td></tr> <tr><td>3rd equation of motion</td><td>2aS = vf² − vi²</td></tr> <tr><td>Gravitational acceleration</td><td>g = 10 m/s²</td></tr> <tr><td>Unit conversion</td><td>1 km/h = 1000/3600 m/s</td></tr> </table> <p>More free notes at Parhai.</p>

9th Class Physics Chapter 2 Notes - Kinematics

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