Linear Motion

Introduction

This chapter introduces the fundamental concepts of linear motion, including how motion is described relative to different frames of reference, the definitions and distinctions between speed and velocity, the concept of acceleration, the physics of free fall, and the use of vectors in describing motion. These principles form the basis for understanding more complex topics in kinematics and dynamics.

Motion Is Relative

Reference Frames

• Motion of objects is always described as relative to something else, known as a reference frame.

• Example: Walking on a road, your motion is relative to Earth, but Earth itself is moving relative to the Sun.

• Your motion relative to the Sun is different from your motion relative to Earth.

Speed

Definition and Calculation

• Speed is defined as the distance covered per unit of travel time.

• Standard SI unit: meters per second (m/s).

• Formula:

• Example: A girl runs 4 meters in 2 seconds. Her speed is .

Average Speed

• Average speed is the total distance covered divided by the total travel time.

• It does not indicate variations in instantaneous speed during the journey.

• Formula:

• Example: Driving 200 km in 2 hours gives an average speed of .

Instantaneous Speed

• Instantaneous speed is the speed at any given instant.

• It is what is shown on a car's speedometer at a specific moment.

• Example: While driving, your speed may vary, but the speedometer shows your instantaneous speed.

Velocity

Definition and Properties

• Velocity describes both the instantaneous speed and the direction of travel.

• It is a vector quantity, meaning it has both magnitude (speed) and direction.

• Velocity is sometimes called "directed speed." Changing either speed or direction changes velocity.

Constant Speed vs. Constant Velocity

• Constant speed: Steady speed, neither increasing nor decreasing.

• Constant velocity: Both constant speed and constant direction (straight-line motion with no acceleration).

• Unless otherwise stated, motion is considered relative to Earth.

Acceleration

Definition and Calculation

• Acceleration is the rate at which velocity changes over time.

• Formulated by Galileo through experiments with inclined planes.

• Acceleration can involve a change in speed, a change in direction, or both.

• Deceleration refers to a decrease in velocity.

• Formula:

• Unit: (velocity unit)/(time unit), e.g., m/s2.

• Example: If a car's speed increases from 40 km/h to 45 km/h in 5 seconds: Change in speed = 45 km/h - 40 km/h = 5 km/h Average acceleration =

Conceptual Points

• An object accelerates when it changes speed or direction (e.g., slowing down or rounding a curve).

• Both velocity and acceleration are rates, but velocity is the rate of change of position, while acceleration is the rate of change of velocity.

• Steeper inclines result in greater accelerations; when the incline is vertical, acceleration is at its maximum (free fall).

• When air resistance is negligible, all objects fall with the same unchanging acceleration.

Free Fall

Definition and Acceleration Due to Gravity

• Free fall refers to motion under the influence of gravity only, with no air resistance.

• On Earth, the acceleration due to gravity is approximately (more precisely, ).

Velocity in Free Fall

• The velocity acquired by an object starting from rest is:

• For :

  • 10 m/s after 1 s

  • 20 m/s after 2 s

  • 30 m/s after 3 s

Distance in Free Fall

• The distance covered by an accelerating object starting from rest is:

• For :

  • 5 m after 1 s

  • 20 m after 2 s

  • 45 m after 3 s

  • 80 m after 4 s

Vectors

Vector Addition and Resultants

• Vectors are quantities that have both magnitude and direction (e.g., velocity, force).

• When combining vectors (such as wind and airplane velocity), use the parallelogram rule to find the resultant vector.

• If two vectors of equal magnitude are perpendicular, the resultant makes a 45-degree angle with each.

• Example: An airplane flying at 80 km/h with a 60 km/h crosswind has a resultant velocity of 100 km/h. If the crosswind is also 80 km/h, the resultant is 113 km/h at 45 degrees.

• Running horizontally at 4 m/s in rain falling vertically at 4 m/s, the resultant velocity of the raindrops relative to you is 5.6 m/s at 45 degrees to the vertical.

Summary Table: Key Equations

Additional info: The notes include conceptual questions and answers to reinforce understanding, as well as practical examples and diagrams to illustrate key points.