Measurement and motion

📌 Key points

1. To measure something small (a thin sheet, a short time), measure many of them and divide, e.g. time 20 swings of a pendulum and divide by 20.
2. Scalars have size only (distance, speed, time, mass, energy, temperature). Vectors have size and direction (force, weight, velocity, acceleration, momentum).
3. Speed = distancetime; average speed = total distancetotal time. Velocity is speed in a given direction.
4. Acceleration = change in velocitytime taken, a = ΔvΔt, in m/s². A negative acceleration is a deceleration.
5. On a distance–time graph the gradient is the speed; a horizontal line means the object is stationary.
6. On a speed–time graph the gradient is the acceleration and the area under the graph is the distance travelled.
7. Near the Earth’s surface, the acceleration of free fall g is approximately constant at 9.8 m/s² (with no air resistance).
8. A falling object speeds up until air resistance equals its weight; the resultant force is then zero and it falls at terminal velocity.
9. Two perpendicular vectors combine by Pythagoras: 6 N east and 8 N north give a resultant of 10 N.

📖 Key terms

Scalar

A quantity with magnitude (size) only.

Vector

A quantity with magnitude and direction.

Speed

Distance travelled per unit time.

Velocity

Speed in a given direction (change in displacement per unit time).

Acceleration

Change in velocity per unit time.

Terminal velocity

The constant velocity reached when the drag force equals the weight.

Resultant

The single vector that has the same effect as two or more vectors together.