Structure of the Atom

4.1 Motion in a Straight Line

Motion in a straight line, also known as linear motion, is the simplest form of motion where an object moves along a straight path. This type of motion is commonly observed in everyday life, such as children running in a swimming race, a ball falling vertically, cars moving on straight roads, or trains running on straight tracks. To analyze such motion, it is essential first to describe the position of the moving object at various instants of time. The position is described relative to a fixed reference point, often called the origin. The position includes both the distance from this reference point and the direction relative to it. If the position of the object changes with time, the object is said to be in motion; if it remains constant, the object is at rest. For example, consider an athlete running on a straight track. Taking the starting point as the reference point (origin 'O'), the athlete's position at different times can be marked along a straight line with positive and negative directions indicated. Positions to the right of the origin are taken as positive, and those to the left as negative. This helps in assigning signs to displacements and velocities, which are vector quantities. Two important quantities to describe motion are distance travelled and displacement. Distance is the total length of the path covered by the object, irrespective of direction, and is a scalar quantity. Displacement is the net change in position of the object from the initial to the final point and is a vector quantity, having both magnitude and direction. For example, if the athlete runs from the origin to point B, then to point A, and back to point B, the total distance travelled is the sum of all path lengths, but the displacement is simply the straight-line distance from the initial to the final position. The SI unit for both distance and displacement is the metre (m). It is important to note that displacement can be zero even when the distance travelled is not zero, such as when the object returns to its starting point. This section also introduces the concept of scalar and vector quantities. Scalars have only magnitude (e.g., distance, speed), while vectors have both magnitude and direction (e.g., displacement, velocity). Understanding these distinctions is crucial for further study of motion. **Table on page 4 (6×4)** | S. No. | Position | Total distance travelled by the ball from O till that position | Displacement of the ball from O till that position | | --- | --- | --- | --- | | 1. | O | 0 cm | 0 cm | | 2. | A | 40 cm | 40 cm in upward direction | | 3. | B | | | | 4. | C | | | | 5. | O | | | **Table on page 8 (4×3)** | Car type | Time interval during which the speed goes from 0 to 100 km h-1 | Magnitude of average acceleration (m s-2) | | --- | --- | --- | | | | | | | | | | | | | **Table on page 10 (2×8)** | Time | 0 s | 1 s | 2 s | 3 s | 4 s | 5 s | 6 s | | --- | --- | --- | --- | --- | --- | --- | --- | | Position | 0 m | 20 m | 40 m | 60 m | 80 m | 100 m | 120 m | **Table on page 11 (8×2)** | Time | Position | | --- | --- | | 0 s | 0 m | | 2 s | 1 m | | 4 s | 4 m | | 6 s | 9 m | | 8 s | 16 m | | 10 s | 25 m | | 12 s | 36 m | **Table on page 14 (8×2)** | Time | Velocity of car | | --- | --- | | 0 s | 0 m s-1 | | 5 s | 2.5 m s-1 | | 10 s | 5.0 m s-1 | | 15 s | 7.5 m s-1 | | 20 s | 10.0 m s-1 | | 25 s | 12.5 m s-1 | | 30 s | 15.0 m s-1 | **Table on page 14 (8×2)** | Time | Velocity of car | | --- | --- | | 0 s | 15.0 m s-1 | | 5 s | 12.5 m s-1 | | 10 s | 10.0 m s-1 | | 15 s | 7.5 m s-1 | | 20 s | 5.0 m s-1 | | 25 s | 2.5 m s-1 | | 30 s | 0 m s-1 |

• Motion in a straight line is called linear motion.
• Position is described relative to a fixed reference point with distance and direction.
• Distance travelled is the total path length and is a scalar quantity.
• Displacement is the net change in position and is a vector quantity.
• Positions to the right of the origin are positive; to the left are negative.
• Displacement can be zero even if distance travelled is not zero.
• 📌 Linear motion: Motion along a straight line.
• 📌 Position: Distance and direction of an object from a reference point.
• 📌 Distance: Total length of the path travelled by an object (scalar).

4.1.3 Average speed and average velocity

Average speed and average velocity are fundamental quantities used to describe how fast an object moves. Average speed is defined as the total distance travelled divided by the time interval during which the motion occurs. Since distance is a scalar quantity, average speed is also a scalar and does not include direction. Mathematically, average speed = total distance travelled / time interval. If an object covers equal distances in equal time intervals, it is said to be in uniform motion with constant speed. Otherwise, the motion is non-uniform, where speed may increase or decrease. Average velocity, on the other hand, is a vector quantity that considers displacement (change in position) over the time interval. It is defined as average velocity = displacement / time interval. The direction of average velocity is the same as the direction of displacement. Both average speed and average velocity have the SI unit metre per second (m/s), though speed is often measured in kilometres per hour (km/h) as well. An example from ancient Indian mathematics illustrates the concept of average speed: two postmen start walking towards each other from a distance of 210 yojanas, one covering 9 yojanas per day and the other 5 yojanas per day. They meet after 15 days, calculated by dividing total distance by the sum of their speeds. The difference between average speed and average velocity is highlighted by an example where a swimmer covers a distance of 50 m in 50 seconds but returns to the starting point, resulting in zero displacement and thus zero average velocity, while average speed remains 1 m/s. Understanding these concepts is crucial for analyzing motion accurately, especially in cases where direction changes, such as circular motion or back-and-forth motion.

• Average speed = total distance travelled / time interval; scalar quantity.
• Average velocity = displacement / time interval; vector quantity with direction.
• Uniform motion involves constant speed; non-uniform motion involves changing speed.
• SI unit for both average speed and velocity is metre per second (m/s).
• Average velocity direction is same as displacement direction.
• Average speed does not provide directional information.
• 📌 Average speed: Scalar quantity representing how fast an object moves regardless of direction.
• 📌 Average velocity: Vector quantity representing rate of change of position with direction.
• 📌 Uniform motion: Motion with constant speed.