Mechanics: Motion

Vectors, kinematics, equations of motion

Scalars and Vectors

Physical quantities are either scalars or vectors. A scalar has magnitude (size) only — e.g. speed (60 km/h), distance (100 m), time (5 s). A vector has both magnitude and direction — e.g. velocity (60 km/h east), displacement (100 m north), force (50 N downward).

Kinematics: Equations of Motion

For uniformly accelerated motion in a straight line: • v = u + at • s = ut + ½at² • v² = u² + 2as Where: u = initial velocity, v = final velocity, a = acceleration, t = time, s = displacement.

Example

Worked Example

A car accelerates uniformly from rest (u = 0) at 2 m·s⁻² for 10 s on a straight road. Find the final velocity: v = u + at = 0 + (2)(10) = 20 m·s⁻¹ Find the displacement: s = ut + ½at² = 0 + ½(2)(10²) = 100 m

Note

Exam Tips

Always list given values and identify the unknown before choosing an equation. Use SI units throughout. Draw a diagram if the problem involves direction. Show every step — marks are awarded for method, not just the final answer.

Key Vocabulary

ScalarA quantity with magnitude only (e.g. speed, distance)

VectorA quantity with both magnitude and direction (e.g. velocity)

DisplacementThe change in position in a specific direction

VelocityThe rate of change of displacement (speed in a direction)

AccelerationThe rate of change of velocity

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