Motion in a Straight Line

Topic-by-topic explanations

1. Introduction

Kinematics studies motion without analysing its cause. Choose an origin and positive direction first; position, displacement, velocity and acceleration depend on that choice.

2. Instantaneous velocity and speed

Average velocity is displacement divided by elapsed time; instantaneous velocity is v=dx/dt. Average speed is total distance/time and instantaneous speed is |v|. Velocity can be negative; speed cannot.

3. Acceleration

Acceleration is the rate of change of velocity, a=dv/dt. Acceleration opposite to velocity reduces speed, while acceleration in the same direction increases it. The sign of acceleration alone does not tell whether an object is slowing.

4. Kinematic equations for uniformly accelerated motion

For constant acceleration, use v=u+at, s=ut+½at², v²=u²+2as and s=(u+v)t/2. Here u is initial velocity, v final velocity, s displacement and t elapsed time.

Formula sheet

Use consistent SI units, identify the system and assumptions, and show the steps of each calculation. Check units and whether the result is physically reasonable.

Worked example

Common errors and revision checklist

The kinematic equations require constant acceleration. Use displacement, not path length, and convert km h⁻¹ to m s⁻¹ before substitution.

• Write the relevant law or relation before substituting values.
• Show units, signs and directions.
• Check assumptions and round only the final result.