A stone was dropped from the top of a cliff and the distance that it fell was measured at the intervals of time as given in the table below. Distance (m) 0 5 20 45 80 100 Time (s) 0 1 2 3 4 4.5 (i) Draw a graph of distance against time in the grid below. A smooth curve through the plotted points is required. (ii) Use the graph to find how far the stone had fallen in 3.5 s. (iii) Calculate the average speed of the falling stone between the second and the fourth second. Give the unit with your answer. (iv) In this experiment is distance fallen directly proportional to time? Justify your answer.

Junior Cycle Science Distance, Speed & Time: A stone was dropped from the top

A stone was dropped from the top of a cliff and the distance that it fell was measured at the intervals of time as given in the table below - Junior Cycle Science - Question a - 2011

Question a

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A stone was dropped from the top of a cliff and the distance that it fell was measured at the intervals of time as given in the table below. Distance (m) 0 5 20 ... show full transcript

Worked Solution & Example Answer:A stone was dropped from the top of a cliff and the distance that it fell was measured at the intervals of time as given in the table below - Junior Cycle Science - Question a - 2011

Step 1

Draw a graph of distance against time

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Answer

To draw the graph:

Plot the points from the table on the grid provided:
- (0, 0)
- (1, 5)
- (2, 20)
- (3, 45)
- (4, 80)
- (4.5, 100)
Connect these points with a smooth curve that represents the distance fallen over time, reflecting the accelerated motion of the stone.

Step 2

Use the graph to find how far the stone had fallen in 3.5 s

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From the graph, locate the value corresponding to 3.5 seconds on the time axis. Draw a horizontal line to intersect the curve. In this case, the distance shown is approximately 60 m. Thus, the stone had fallen 60 m in 3.5 s.

Step 3

Calculate the average speed of the falling stone between the second and the fourth second

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To find the average speed between the second and fourth seconds:

The distance fallen at 2 seconds is 20 m.
The distance fallen at 4 seconds is 80 m.
Average speed is calculated using the formula: $ext{Average Speed} = \frac{\text{Distance}_{final} - \text{Distance}_{initial}}{\text{Time}_{final} - \text{Time}_{initial}}$ Therefore: $\text{Average Speed} = \frac{80 m - 20 m}{4 s - 2 s} = \frac{60 m}{2 s} = 30 m/s$

Step 4

In this experiment is distance fallen directly proportional to time? Justify your answer.

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In this experiment, distance fallen is not directly proportional to time. This can be observed by the shape of the graph. If the relationship were directly proportional, the graph would be a straight line, indicating a constant speed. However, the graph is curved, suggesting that the stone is accelerating due to gravity as it falls, therefore demonstrating a non-linear relationship.

A stone was dropped from the top of a cliff and the distance that it fell was measured at the intervals of time as given in the table below - Junior Cycle Science - Question a - 2011

Worked Solution & Example Answer:A stone was dropped from the top of a cliff and the distance that it fell was measured at the intervals of time as given in the table below - Junior Cycle Science - Question a - 2011

Draw a graph of distance against time

Use the graph to find how far the stone had fallen in 3.5 s

Calculate the average speed of the falling stone between the second and the fourth second

In this experiment is distance fallen directly proportional to time? Justify your answer.

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