Motion in a Straight Line - Class 11 Physics

Motion in a Straight Line

1. What is Motion?

Motion is the change in position of an object with time. If it occurs along a straight line, it's called rectilinear motion or motion in a straight line.

2. Frame of Reference

A system used to measure the position and motion of a body. It includes:

  • A reference point (origin)
  • Coordinate axes (x, y, z)
  • A clock to measure time

3. Rest and Motion

  • Rest: Object doesn’t change position with respect to reference.
  • Motion: Object changes position with respect to reference.

4. Distance and Displacement

QuantityDistanceDisplacement
TypeScalarVector
DefinitionTotal path lengthShortest path between two points
SignAlways positiveCan be +, −, or 0

5. Speed and Velocity

QuantitySpeedVelocity
TypeScalarVector
DefinitionDistance / TimeDisplacement / Time
UniformConstant speedConstant magnitude & direction

6. Acceleration

Rate of change of velocity with respect to time.

Formula: a = (v - u) / t

  • Positive acceleration: Speeding up
  • Negative acceleration: Slowing down (Retardation)

7. Types of Motion

  • Uniform Motion: Equal displacement in equal intervals of time.
  • Non-uniform Motion: Unequal displacement in equal time intervals.

8. Graphs of Motion

  • Distance-Time Graph: Slope = speed; Curve = acceleration
  • Velocity-Time Graph: Slope = acceleration; Area = displacement

9. Equations of Motion (Uniform Acceleration)

  • v = u + at
  • s = ut + (1/2)at²
  • v² = u² + 2as
  • s = (v + u)/2 × t

Where:

  • u = initial velocity
  • v = final velocity
  • a = acceleration
  • t = time
  • s = displacement

10. Relative Velocity

  • If objects move in the same direction: vrel = v₁ - v₂
  • If in opposite directions: vrel = v₁ + v₂

11. Free Fall

Motion under the influence of gravity alone.

  • Acceleration due to gravity: g = 9.8 m/s²
  • Use motion equations with a = g when falling downward
  • Use a = -g when moving upward

12. Sign Conventions

  • Upward or Right → Positive
  • Downward or Left → Negative
  • Displacement, velocity, and acceleration follow this rule

13. Instantaneous vs Average

  • Average velocity: Over a time interval
  • Instantaneous velocity: At a specific instant

14. Position-Time Graph

  • Straight line → Uniform motion
  • Curved line → Accelerated motion
  • Slope = Velocity

15. Important Points

  • Distance ≥ Displacement
  • Speed ≥ Velocity
  • Displacement can be zero; distance cannot
  • Negative acceleration = Retardation
  • Area under velocity-time graph = Displacement