Science · Class 9 · Motion

Describing Motion and the Equations of Motion

Aim: Describe the motion of an object using distance, displacement, speed, velocity, and acceleration, and apply the equations of motion.
  • Distance — total path length covered (scalar)
  • Displacement — shortest straight-line change in position, with direction (vector)
  • Speed — distance covered per unit time
  • Velocity — displacement per unit time, in a given direction
  • Acceleration — rate of change of velocity
40 min lesson

Motion · Concept 1 of 8

Distance vs. displacement

  • Distance: total length of the actual path travelled — always positive, no direction
  • Displacement: shortest distance from start to end point, with direction — can be zero even if distance travelled is large
  • Example: running one full lap of a 400 m track — distance = 400 m, displacement = 0 m

Motion · Concept 2 of 8

Speed vs. velocity

  • Speed = distance / time (scalar — magnitude only)
  • Velocity = displacement / time (vector — magnitude and direction)
  • Uniform velocity: equal displacements in equal time intervals, same direction

Motion · Concept 3 of 8

Average speed and average velocity

  • Average speed = total distance / total time
  • Average velocity = total displacement / total time
  • These can differ significantly when direction changes during the journey

Motion · Concept 4 of 8

What is acceleration?

  • Acceleration = change in velocity / time taken
  • Positive acceleration: speeding up in the direction of motion
  • Negative acceleration (retardation): slowing down
  • Uniform acceleration: velocity changes by equal amounts in equal time intervals

Motion · Concept 5 of 8

The three equations of motion

  • v = u + at (velocity after time t)
  • s = ut + 1/2 at^2 (distance covered in time t)
  • v^2 = u^2 + 2as (relates velocity and distance, no time needed)
  • u = initial velocity, v = final velocity, a = acceleration, t = time, s = distance

Motion · Concept 6 of 8

Worked example

  • A car starts from rest (u = 0) and accelerates at 2 m/s^2 for 5 s
  • Find v: v = u + at = 0 + (2)(5) = 10 m/s
  • Find s: s = ut + 1/2 at^2 = 0 + 1/2(2)(25) = 25 m

Motion · Concept 7 of 8

Reading motion graphs

  • Distance-time graph: slope gives speed; a straight line means uniform speed
  • Velocity-time graph: slope gives acceleration; area under the graph gives distance covered
  • A flat velocity-time line means constant velocity (zero acceleration)

Motion · Concept 8 of 8

Uniform circular motion

  • Moving in a circle at constant speed still counts as accelerated motion
  • Because the direction of velocity keeps changing, even though speed stays the same
  • Examples: a satellite orbiting Earth, a stone whirled on a string

Quick Recap

Check Your Understanding

  1. 1A student walks 3 m east then 4 m north. What is the distance travelled and what is the displacement?
  2. 2Write the three equations of motion and label each symbol.
  3. 3Why is motion in a circle at constant speed still considered accelerated motion?