kinematics notes part 1

Kinematics

Distance & Displacement

Distance

• Definition: Distance refers to the total path length traveled by an object, independent of direction.

• Characteristics: It is a scalar quantity, meaning it only includes magnitude.

• Example: In a 300 m race on a 400 m track, if the athletes run the total distance of 300 m, this value remains constant irrespective of their position.

Displacement

• Definition: Displacement measures how far an object is from its starting position and includes a direction.

• Characteristics: Displacement is a vector quantity; it describes both magnitude and direction.

• Example: An athlete running 300 m towards a finish line may end up 100 m from their starting point. In this context, while the distance is 300 m, the displacement is 100 m to the finish line.

• Comparison: The difference between distance and displacement can be understood through a hiking example: a person may travel a longer distance in the woods but only be a few miles away from their starting point as the crow flies (displacement).

Key Differences between Distance and Displacement

• Distance: A scalar quantity with only magnitude, independent of direction.

• Displacement: A vector quantity encompassing both magnitude and direction. For instance, if running 300 m results in a displacement of 100 m to the right, if the athlete runs 400 m, their displacement could return to 0 m, indicating no change in position from the starting point.

Speed & Velocity

Speed

• Definition: The speed of an object is the measure of distance traveled in a specific time.

• Characteristics: Speed is a scalar quantity because it consists only of magnitude and has no direction.

• Formula: Average speed can be calculated using the equation:

  [ \text{Average Speed} = \frac{\text{Total Distance}}{\text{Time Taken}} ]

• Units: The SI unit for speed is meters per second (ms⁻¹), but it can also be measured in kilometers per hour (km/h) or miles per hour (mph).

Velocity

• Definition: Velocity describes the rate of change of an object's position and includes direction.

• Characteristics: As a vector, it represents both magnitude and directional movement.

• Example: If a car travels 20 m/s to the east, its speed is 20 m/s, but its velocity is 20 m/s EAST. Similarly, if it travels 20 m/s to the west, its velocity is 20 m/s WEST; both have the same speed but differing velocities.

Instantaneous Speed & Velocity

• Instantaneous Speed/Velocity: This refers to the speed or velocity of an object at a specific moment. Instantaneous measurements can be taken from a displacement-time graph by drawing a tangent at the desired time to find the gradient.

Acceleration

Definition

• Acceleration: Acceleration is defined as the rate of change of velocity, representing how much an object's speed increases or decreases over time.

• Characteristics: Acceleration is a vector quantity measured in meters per second squared (ms⁻²).

• Formula: The average acceleration can be calculated using:

  [ \text{Average Acceleration} = \frac{\text{Change in Velocity}}{\text{Time Taken}} ]

• With a change in velocity defined as the final velocity minus the initial velocity (( , \Delta v = v - u )).

Key Equations

• The fundamental relation between displacement, velocity, and acceleration in physics is shown via:

  [ v = \frac{\Delta x}{\Delta t} ]

  [ a = \frac{\Delta v}{\Delta t} ]

Instantaneous Acceleration

• Instantaneous Acceleration: It can be found at a specific instance and determined from a velocity-time graph, similar to how instantaneous velocity is calculated from a displacement-time graph.

Direction of Acceleration

• Types of Acceleration:

  • Positive acceleration (speeding up).

  • Negative acceleration (decelerating or slowing down), which can also be referred to as deceleration. Acceleration can be negative if the object is moving in a negative direction.

Worked Examples

• An example includes calculating the deceleration of a Japanese bullet train, determining change in velocity and elucidating slowing down with negative values.

This overview covers essential elements of kinematics, focusing on distance, displacement, speed, velocity, and acceleration along with significant examples for understanding these concepts in physics.