Calculate the average speed for the whole journey

Question

ScanSolve AI Tutor · Accepted Answer

To calculate the average speed for the whole journey from a speed-time graph, we need to find the total distance traveled and divide it by the total time taken.

Determine the total time and maximum speed from the graph.
The graph shows that the journey starts at $t=0$ and ends at $t=20$ .
The maximum speed reached is 15 units (from the y-axis).
The total time taken for the journey is 20 units.
Calculate the total distance traveled.
The total distance traveled is represented by the area under the speed-time graph. The shape of the graph is a trapezium.
The formula for the area of a trapezium is $\frac{1}{2} \times (\text{sum of parallel sides}) \times \text{height}$ .
In this graph:
- The length of the top parallel side (constant speed duration) is $15 - 5 = 10$ units.
- The length of the bottom parallel side (total time duration) is $20 - 0 = 20$ units.
- The height of the trapezium (maximum speed) is 15 units.
$\text{Total Distance} = \frac{1}{2} \times (10 + 20) \times 15$ $\text{Total Distance} = \frac{1}{2} \times (30) \times 15$ $\text{Total Distance} = 15 \times 15$ $\text{Total Distance} = 225 \text{ units}$
Calculate the average speed.
The average speed is given by the formula:
$\text{Average Speed} = \frac{\text{Total Distance}}{\text{Total Time}}$ $\text{Average Speed} = \frac{225}{20}$ $\text{Average Speed} = 11.25 \text{ units}$
The average speed for the whole journey is $\text{11.25 units}$ .

Calculate the average speed for the whole journey

Answer

Step-by-step solution

Determine the total time and maximum speed from the graph.

Calculate the total distance traveled.

Calculate the average speed.

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