MATHWITHCYE Measurement & Geometry

Graphs of Motion (Graf Gerakan)

Analyze distance-time and speed-time graphs, interpret rates of change, and calculate total distance via area.

s-t

Distance - Time Graph ($s-t$)

Plots the distance from a fixed origin against time.

Gradient: $\frac{\Delta s}{\Delta t} = \text{Speed (Laju)}$
Horizontal Line (Gradient = 0): Stationary / At rest (Pegun).
Negative Gradient: Moving back towards the starting point.
Average Speed: $\frac{\text{Total Distance}}{\text{Total Time}}$
v-t

Speed - Time Graph ($v-t$)

Plots instantaneous speed against time.

Gradient: $\frac{\Delta v}{\Delta t} = \text{Acceleration (Pecutan)}$
Negative Gradient: Deceleration (Nyahpecutan).
Horizontal Line: Uniform / constant speed (Pecutan = 0).
Area Under Graph = Total Distance Travelled (Jarak Dilalui)!

Area Under Graph Geometry Cheat Sheet

Triangle:
$$\text{Area} = \frac{1}{2} \times \text{base} \times \text{height}$$
Trapezium:
$$\text{Area} = \frac{1}{2}(a + b) \times h$$
Rectangle:
$$\text{Area} = \text{length} \times \text{width}$$