Speed (sec)position (cm per sec)
0,0.0
1,8.0
2,16.0
3,24.0
Based on the given data, the speed of the object can be calculated as follows:
Speed (cm/sec) = Change in position (cm) / Change in time (sec)
For the first interval:
Change in position = 8.0 cm - 0.0 cm = 8.0 cm
Change in time = 1 sec - 0 sec = 1 sec
Speed = 8.0 cm / 1 sec = 8.0 cm/sec
For the second interval:
Change in position = 16.0 cm - 8.0 cm = 8.0 cm
Change in time = 2 sec - 1 sec = 1 sec
Speed = 8.0 cm / 1 sec = 8.0 cm/sec
For the third interval:
Change in position = 24.0 cm - 16.0 cm = 8.0 cm
Change in time = 3 sec - 2 sec = 1 sec
Speed = 8.0 cm / 1 sec = 8.0 cm/sec
Therefore, the speed of the object remains constant at 8.0 cm/sec throughout the given time intervals.
To find the speed in cm per second for each position, you can find the difference in position between consecutive time intervals.
For example, in the given data:
- From time 0 to time 1: The position changes from 0.0 cm to 8.0 cm. So, the speed is (8.0 - 0.0) cm/sec = 8.0 cm/sec.
- From time 1 to time 2: The position changes from 8.0 cm to 16.0 cm. So, the speed is (16.0 - 8.0) cm/sec = 8.0 cm/sec.
- From time 2 to time 3: The position changes from 16.0 cm to 24.0 cm. So, the speed is (24.0 - 16.0) cm/sec = 8.0 cm/sec.
Therefore, the speed at all positions is 8.0 cm/sec.
To find the relationship between speed and position in this given data, we can observe that the position increases by 8 centimeters every second. This indicates a constant speed of 8 centimeters per second.
To understand this relationship mathematically, we can use the formula for average speed:
Speed = Change in position / Change in time
Let's calculate the speed for the given data points:
For the first data point (0, 0.0), there is no change in position since the time elapsed is 0 seconds. Therefore, the speed is 0 cm/s.
For the second data point (1, 8.0), the change in position is 8 cm and the change in time is 1 second. So, the speed is:
Speed = (8 cm - 0 cm) / (1 s - 0 s) = 8 cm/s
Similarly, for the third data point (2, 16.0), the change in position is 16 cm and the change in time is 2 seconds. So, the speed is:
Speed = (16 cm - 8 cm) / (2 s - 1 s) = 8 cm/s
Finally, for the fourth data point (3, 24.0), the change in position is 24 cm and the change in time is 3 seconds. So, the speed is:
Speed = (24 cm - 16 cm) / (3 s - 2 s) = 8 cm/s
Hence, as we observed earlier, the speed remains constant at 8 centimeters per second in this given data.