⚡ PHYSICS · CLASS 9

Motion

3 equations of motion animated — distance, velocity, acceleration

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🚀 What is Motion?

An object is in motion when its position changes with time. Key terms:

  • Distance (d) — total path length covered (scalar)
  • Displacement (s) — shortest distance from start to end (vector)
  • Speed — distance / time (scalar)
  • Velocity (v) — displacement / time (vector)
  • Acceleration (a) — change in velocity / time
Basic Formulas Speed = Distance/Time    Velocity = Displacement/Time
Acceleration = (v − u) / t
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📊 Distance–Time & Velocity–Time Graphs

A straight line on d-t graph → uniform motion. Slope of v-t graph → acceleration. Watch both graphs draw!

Slope of d-t graph = velocity    Slope of v-t graph = acceleration
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⚡ The 3 Equations of Motion

These equations apply to uniform acceleration in a straight line. Master all three!

1st Equation
v = u + at

Relates final velocity, initial velocity, acceleration and time

2nd Equation
s = ut + ½at²

Relates displacement, initial velocity, acceleration and time

3rd Equation
v² = u² + 2as

Relates velocities, acceleration and displacement (no time)

  • u = initial velocity, v = final velocity
  • a = acceleration, s = displacement, t = time
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📝 Deriving v = u + at

1

Definition of acceleration

a = (v − u) / t

2

Multiply both sides by t

at = v − u

3

Rearrange

v = u + at ✓

v = u + at
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✏️ Solved Example

Q: A car starts from rest and accelerates at 4 m/s². Find its velocity and distance after 5 seconds.

1

Given

u = 0 (starts from rest), a = 4 m/s², t = 5 s

2

Find v using 1st equation

v = u + at = 0 + 4×5 = 20 m/s

3

Find s using 2nd equation

s = ut + ½at² = 0 + ½×4×25 = 50 m

v = 20 m/s    s = 50 m
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🧠 Quick Quiz

Q: A body starts with u = 10 m/s and decelerates at 2 m/s². When does it stop?

Motion mastered! 🎉

← Integration