define and use distance, displacement, speed, velocity and acceleration

Equations of Motion

What is Motion?

Motion is the change of position of an object over time. In physics we describe this change using distance, displacement, speed, velocity and acceleration.

Distance & Displacement

Distance (scalar) – total length travelled, regardless of direction.

Displacement (vector) – straight‑line change from start to finish, with direction.

🛤️ Analogy: Distance is like the total miles you drive on a road trip; displacement is the straight line from your home to the final city.

Speed & Velocity

Speed (scalar) – distance divided by time.

Velocity (vector) – displacement divided by time.

🚗 Example: A car covers 120 m in 30 s → speed = 4 m s⁻¹. If it ends 120 m east of start, velocity = 4 m s⁻¹ east.

Acceleration

Acceleration is the rate of change of velocity.

⚡ Example: A bike speeds up from 0 to 10 m s⁻¹ in 5 s → acceleration = 2 m s⁻².

Basic Equations of Motion (constant acceleration)

EquationMeaning
\$s = ut + \tfrac{1}{2}at^2\$Displacement from initial velocity u, acceleration a, over time t.
\$v = u + at\$Final velocity after time t.
\$v^2 = u^2 + 2as\$Relates velocities and displacement without time.

Step‑by‑Step Example

  1. Find initial velocity u (often 0).

  2. Determine acceleration a (positive if speeding up).

  3. Insert values into the chosen equation.

  4. Check units: m, s, m s⁻¹, m s⁻².

  5. Verify sign: use right‑hand rule for direction.

Exam Tip 💡

Always write the full equation before substituting numbers. This reduces mistakes and shows your working clearly.

Common Mistakes to Avoid

  • Confusing distance with displacement.

  • Using speed instead of velocity when direction matters.

  • Ignoring the sign of acceleration (negative for deceleration).

  • Forgetting to convert units (e.g., km h⁻¹ to m s⁻¹).

Quick Revision Checklist

  • ✓ Know the difference between scalar and vector quantities.

  • ✓ Memorise the three main kinematic equations.

  • ✓ Practice unit conversions.

  • ✓ Draw a simple diagram to visualise displacement and velocity.