Motion in a Straight Line

Motion in a Straight Line

Definition

• Motion in a straight line, also known as rectilinear motion, is a type of motion where an object moves in a straight line.

Displacement and Distance

• Displacement: The shortest distance between the initial and final positions of an object.
• Distance: The total length of the path traveled by an object.
• Example: A car travels from A to B and then back to A. The displacement is zero, but the distance traveled is the total length of the path.

Velocity and Speed

• Velocity: The rate of change of displacement with respect to time.
• Speed: The rate of change of distance with respect to time.
• Velocity is a vector quantity, while speed is a scalar quantity.

Acceleration

• Acceleration: The rate of change of velocity with respect to time.
• Can be positive (acceleration), negative (deceleration), or zero (uniform motion).

Equations of Motion

• First Equation of Motion: v = u + at
  • v: final velocity
  • u: initial velocity
  • a: acceleration
  • t: time
• Second Equation of Motion: s = ut + (1/2)at^2
  • s: displacement
  • u: initial velocity
  • a: acceleration
  • t: time
• Third Equation of Motion: v^2 = u^2 + 2as
  • v: final velocity
  • u: initial velocity
  • a: acceleration
  • s: displacement

Graphical Analysis

• Distance-Time Graph: A straight line indicates uniform motion.
• Velocity-Time Graph: A straight line indicates uniform acceleration.
• Acceleration-Time Graph: A straight line indicates constant acceleration.

Key Concepts

• Uniform motion: constant velocity
• Non-uniform motion: changing velocity
• Acceleration can be positive, negative, or zero
• Displacement and distance are not always equal

Motion in a Straight Line

Definition

• Rectilinear motion occurs when an object moves in a straight line.

Displacement and Distance

• Displacement is the shortest distance between an object's initial and final positions.
• Distance is the total length of an object's path.
• Displacement and distance are not always equal, as an object can travel a long distance but end up back at its starting point, resulting in zero displacement.

Velocity and Speed

• Velocity is the rate of change of displacement with respect to time, and is a vector quantity.
• Speed is the rate of change of distance with respect to time, and is a scalar quantity.
• Velocity and speed are not always equal, as an object can change direction while maintaining a constant speed.

Acceleration

• Acceleration is the rate of change of velocity with respect to time, and can be positive, negative, or zero.
• Positive acceleration indicates an increase in velocity.
• Negative acceleration indicates a decrease in velocity, also known as deceleration.
• Zero acceleration indicates uniform motion.

Equations of Motion

• The first equation of motion is v = u + at, where v is final velocity, u is initial velocity, a is acceleration, and t is time.
• The second equation of motion is s = ut + (1/2)at^2, where s is displacement, u is initial velocity, a is acceleration, and t is time.
• The third equation of motion is v^2 = u^2 + 2as, where v is final velocity, u is initial velocity, a is acceleration, and s is displacement.

Graphical Analysis

• A straight line on a distance-time graph indicates uniform motion.
• A straight line on a velocity-time graph indicates uniform acceleration.
• A straight line on an acceleration-time graph indicates constant acceleration.

Key Concepts

• Uniform motion occurs when velocity is constant.
• Non-uniform motion occurs when velocity is changing.
• Acceleration can cause an object to speed up, slow down, or change direction.