Speed-Time Graphs

Speed-Time Graphs

• The gradient of a distance-time graph is the velocity
• The gradient of a speed-time graph is the acceleration
• The area under a speed-time graph is the distance travelled

Calculating Acceleration

\[ \begin{aligned} a &= \frac{rise}{run} \cr a &= \frac{\Delta v}{\Delta t} \cr a &= \frac{v_{f} - v_{i}}{t_{f} - t_{i}} \end{aligned} \]

Finding the Distance

• Calculate the area under the speed-time graph to find the distance travelled
• Break it up into rectangles & triangles to calculate the area
• Finding area of a rectangle is \(A = B \times H\)
• On the graph \(d = t \times v\)
• This should look familiar from \(v=\frac{d}{t} \rightarrow d = v \times t\)!