Equations of Motion

Introduction

The equations of motion describe the relationship between displacement, velocity, acceleration, and time for uniformly accelerated motion. These equations are very useful in solving numerical problems related to motion.

First Equation of Motion

Equation: v = u + at

This equation gives the final velocity of an object when initial velocity, acceleration, and time are known.

  • v = Final velocity (m/s)
  • u = Initial velocity (m/s)
  • a = Acceleration (m/s²)
  • t = Time (s)

Example: A car starts with velocity 5 m/s and accelerates at 2 m/s² for 4 s.

v = 5 + (2 × 4) = 13 m/s

Illustration:

Start End u = 5 m/s v = 13 m/s a = 2 m/s², t = 4 s

Second Equation of Motion

Equation: s = ut + ½at²

This equation gives the displacement of an object when initial velocity, acceleration, and time are known.

  • s = Displacement (m)
  • u = Initial velocity (m/s)
  • a = Acceleration (m/s²)
  • t = Time (s)

Example: u = 6 m/s, a = 3 m/s², t = 5 s

s = (6 × 5) + ½ × 3 × 25 = 30 + 37.5 = 67.5 m

Illustration:

Start End u = 6 m/s a = 3 m/s² t = 5 s s = 67.5 m

Third Equation of Motion

Equation: v² = u² + 2as

This equation relates velocity, acceleration, and displacement without using time.

  • v = Final velocity (m/s)
  • u = Initial velocity (m/s)
  • a = Acceleration (m/s²)
  • s = Displacement (m)

Example: u = 8 m/s, a = 2 m/s², s = 50 m

v² = 64 + 200 = 264 → v ≈ 16.25 m/s

Illustration:

Start End u = 8 m/s v ≈ 16.25 m/s a = 2 m/s², s = 50 m

Important Points

  • These equations are valid only for uniform acceleration.
  • First equation gives velocity with time.
  • Second equation gives displacement with time.
  • Third equation is used when time is not given.

Conclusion

Equations of motion are very important in physics. They help us find unknown quantities like velocity, displacement, and acceleration in a simple way. These equations are widely used in solving numerical problems of motion.

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