Question

A ball travels at a constant speed of 6 meters per second along a frictionless surface. Which table correctly shows what a student may have measured and recorded if they watched this ball in motion over a 10-second time period?

Table 1- Time(seconds): 2 4 6 8 10 Distance(meters): 12 24 36 48 60
Table 2- Time(seconds): 2 4 6 8 10 Distance(meters): 12 20 22 30 32
Table 3- Time(seconds): 2 4 6 8 10 Distance(meters): 6 12 24 36 42
Table 4- Time(seconds): 2 4 6 8 10 Distance(meters): 24 34 44 54 64

Answer 1

To determine which table accurately reflects the motion of a ball traveling at a constant speed of 6 meters per second, we can calculate the distance the ball would travel at this speed over each given time interval.

The formula for distance (d) is:

\[ d = \text{speed} \times \text{time} \]

In this case, the speed is 6 meters per second.

Now, let's calculate the distance for each time interval:

- At 2 seconds:
\[ d = 6 \, \text{m/s} \times 2 \, \text{s} = 12 \, \text{meters} \]

- At 4 seconds:
\[ d = 6 \, \text{m/s} \times 4 \, \text{s} = 24 \, \text{meters} \]

- At 6 seconds:
\[ d = 6 \, \text{m/s} \times 6 \, \text{s} = 36 \, \text{meters} \]

- At 8 seconds:
\[ d = 6 \, \text{m/s} \times 8 \, \text{s} = 48 \, \text{meters} \]

- At 10 seconds:
\[ d = 6 \, \text{m/s} \times 10 \, \text{s} = 60 \, \text{meters} \]

Now, let's compare these results with the tables:

- **Table 1**:
- Time (s): 2, 4, 6, 8, 10
- Distance (m): 12, 24, 36, 48, 60 (Valid)

- **Table 2**:
- Time (s): 2, 4, 6, 8, 10
- Distance (m): 12, 20, 22, 30, 32 (Not valid)

- **Table 3**:
- Time (s): 2, 4, 6, 8, 10
- Distance (m): 6, 12, 24, 36, 42 (Not valid)

- **Table 4**:
- Time (s): 2, 4, 6, 8, 10
- Distance (m): 24, 34, 44, 54, 64 (Not valid)

The only table that correctly shows the distances the ball would travel at a constant speed of 6 meters per second over the 10-second period is **Table 1**.