Describing motion
| English | Chinese | Pinyin |
|---|---|---|
| distance | 距离 | jù lí |
| displacement | 位移 | wèiyí |
| speed | 速率 | sùlǜ |
| velocity | 速度 | sùdù |
| acceleration | 加速度 | jiāsùdù |
| gradient | 斜率 | xié lǜ |
| deceleration | 减速度 | jiǎn sù dù |
| tangent | 切线 | qiè xiàn |
There and back
- A runner does one lap of a $400\ \text{m}$ track and stops where they started.
- Distance 距离 travelled: $400\ \text{m}$. Displacement 位移: $0$.
- Describing motion well starts with getting words like these exactly right.
Five key words
- distance (scalar) — total path length; displacement (vector) — straight line, start to end.
- speed 速率 (scalar) — rate of change of distance; velocity 速度 (vector) — rate of change of displacement.
- acceleration 加速度 (vector) — rate of change of velocity. Units: $\dfrac{\text{m}}{\text{s}}$ and $\dfrac{\text{m}}{\text{s}^2}$.
Velocity–time graph — gradient 斜率 gives acceleration, area gives displacement
The velocity–time graph
v = u + at
On a speed–time graph the gradient is the acceleration and the area underneath is the distance travelled.
The rate of change of velocity with time is called ____.
Acceleration is how fast the velocity changes — a vector, in $\dfrac{\text{m}}{\text{s}^2}$.
Which quantity is the rate of change of displacement?
Velocity is the rate of change of displacement (a vector). Speed is the rate of change of distance (a scalar).
Deceleration 减速度 is not a new quantity — it is just acceleration pointing opposite to the velocity (a negative acceleration).
Experimental set-up for measuring the acceleration due to free fall
Deceleration is a completely separate quantity from acceleration.
No — deceleration is just acceleration in the opposite direction to the motion (a negative acceleration).
Two graphs do the work
- Most motion questions use a displacement–time or a velocity–time graph.
- The whole skill is knowing what the gradient and the area mean on each.
Displacement–time graph
- The gradient (steepness) = the velocity.
- Flat → at rest. Straight → constant velocity. Curved → take a tangent 切线.
On a displacement–time graph, a flat (horizontal) line means the object is at rest.
A flat line has zero gradient, and the gradient is the velocity — so the velocity is zero (at rest).
Velocity–time graph
- The gradient = the acceleration.
- The area under the line = the displacement.
Match each graph feature to what it tells you.
Gradients give rates of change; the area under a velocity–time graph builds up the displacement.
Displacement from the area
- Split the area into triangles and rectangles, then add them up.
- Triangle $= \tfrac{1}{2} \times \text{base} \times \text{height}$; rectangle $= \text{base} \times \text{height}$.
A car speeds up from rest to $20\ \dfrac{\text{m}}{\text{s}}$ in $10\ \text{s}$ (a straight velocity–time line). How far does it travel?
Displacement = area under the line = $\tfrac{1}{2} \times \text{base} \times \text{height} = \tfrac{1}{2} \times 10 \times 20 = 100\ \text{m}$.
You've got it
- distance & speed are scalars; displacement, velocity & acceleration are vectors
- displacement–time gradient = velocity; velocity–time gradient = acceleration
- area under a velocity–time graph = the displacement