Motion, force and the discipline of units

Distance measures the length of a path. Displacement measures the change in position with a direction. Average speed is total distance divided by elapsed time; average velocity uses displacement instead. A traveller can return to the starting point with a non-zero distance travelled but zero displacement.

Worked example: a vehicle covers 180 metres in 12 seconds. Average speed = 180/12 = 15 m/s. This does not mean its instantaneous speed was 15 m/s throughout the journey.

Acceleration is change in velocity divided by time. If velocity increases from 5 m/s to 17 m/s in 4 seconds, average acceleration is (17 - 5)/4 = 3 m/s^2. Use the change, not the final velocity alone.

Newton’s second law relates resultant force to mass and acceleration: F = ma. A 6 kg body accelerating at 2 m/s^2 needs a resultant force of 12 N. Resultant force means the combined effect of the forces acting on the body, not necessarily one individual applied force.

Convert quantities before substitution. To convert km/h to m/s, divide by 3.6. Thus 54 km/h equals 15 m/s. Keep the unit beside every intermediate value; it makes mistakes easier to detect.

Practice:
1. Find average speed for 96 m in 8 s.
2. Find acceleration when velocity changes from 2 to 14 m/s in 6 s.
3. Find the resultant force for 4 kg accelerating at 3 m/s^2.
4. Convert 36 km/h to m/s.

Answers: 1 12 m/s; 2 2 m/s^2; 3 12 N; 4 10 m/s.

Check whether the question asks for speed, velocity, distance or displacement before using a formula. In your error log, identify conceptual confusion separately from conversion mistakes. For a practical measurement exercise, repeat the observation and describe uncertainty rather than presenting a timed value as perfectly exact.