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

1 answer

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.