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The graph below shows the distance travelled along a track by Ann over the course of a race - Junior Cycle Mathematics - Question 5 - 2016
Question 5
The graph below shows the distance travelled along a track by Ann over the course of a race. The graph is in two sections, labelled A and B. (i) Show that Ann’s spe... show full transcript
Worked Solution & Example Answer:The graph below shows the distance travelled along a track by Ann over the course of a race - Junior Cycle Mathematics - Question 5 - 2016
Step 1
Show that Ann’s speed in section A is 5 metres per second.
Answer
To find Ann's speed in section A, we can use the formula:
ext{Speed} = rac{ ext{Distance}}{ ext{Time}}From the graph, the distance covered in section A is 300 meters and the time taken is 60 seconds. Plugging these values into the formula gives us:
ext{Speed} = rac{300 ext{ m}}{60 ext{ s}} = 5 ext{ m/s}Thus, Ann’s speed in section A is 5 metres per second.
Step 2
Find Ann’s speed in section B, in metres per second.
Answer
For section B, the distance travelled is 100 meters and the time taken is 40 seconds. Again, using the formula for speed:
ext{Speed} = rac{ ext{Distance}}{ ext{Time}} = rac{100 ext{ m}}{40 ext{ s}} = 2.5 ext{ m/s}Therefore, Ann’s speed in section B is 2.5 metres per second.
Step 3
Step 4
Sketch the graph of Erik’s speed during the race.
Answer
To sketch Erik's speed graph, observe the distance graph of Erik. The speed should be derived from the slope of the distance graph. When Erik travels steadily, the speed is constant, which we represent as a horizontal line at that speed value.
Identify the time intervals where Erik’s speed is constant and where it changes to indicate acceleration or deceleration. For sections where Erik is stationary, the speed will be zero, represented by a horizontal line at the zero speed level in the speed graph.