Question

Plot a distance-time graph of the tip of the second hand of a clock by selecting $4\mathrm{points}$ on the x-axis and y-axis respectively. The circumference of the circle traced by the second hand is $64\mathrm{cm}$.

Answer 1

Step 1: Distance-time graph

A distance-time graph, as the name implies, shows the distance traveled by an item in a given amount of time.

1. The Y-axis in this graph represents distance, while the X-axis represents time.
2. If indeed the graph is a straight line, the object's motion is uniform. The slope of the straight-line graph remains constant regardless of the interval used. This means that an object's speed stays unchanged in uniform motion.

Step 2: Construction of graph

The circumference traced by the second hand in $60\mathrm{seconds}$ is $64\mathrm{cm}$.

The circumference traced by the second in one second is$\frac{64}{60}\mathrm{cm}$.

Therefore, the circumference traced by the second hand in $15\mathrm{seconds}$ is $\frac{64}{60}\times 15=16\text{cm}$.

Similarly, the circumference traced by the second hand in $30\mathrm{seconds}$ is $32\mathrm{cm}$.

Before constructing the graph, simply take four clock points at $3,6,9,$ and $12\mathrm{hours}$ as shown in the figure below. Each point represents the quadrant of a circle.

1. The second-hand travel $16\mathrm{cm}$ and takes $15\mathrm{seconds}$ to reach point A.
2. Point B takes $30\mathrm{seconds}$ and the second-hand covers $32\mathrm{cm}$.
3. Point C takes $45\mathrm{seconds}$ to complete and covers $48\mathrm{cm}$.
4. Point D appears to take $60\mathrm{seconds}$ to complete and cover $64\mathrm{cm}$.

Step 3: Distance-time graph