the following data were obtained for the position of a ball as it rolled along a straight track
DISPLACEMENT (CM) TIME
2.90 0.60
7.40 2.10
11.00 3.30
22.70 7.20
31.10 10.00
To analyze the data and find the relationship between displacement and time for the ball rolling along a straight track, we can plot a graph of displacement (y-axis) against time (x-axis). We can then calculate the slope of the line to determine the ball's speed.
First, let's plot the given data points on a graph:
DISPLACEMENT (CM) | TIME
2.90 | 0.60
7.40 | 2.10
11.00 | 3.30
22.70 | 7.20
31.10 | 10.00
Now, on a sheet of graph paper or using a graphing tool, create a Cartesian coordinate system with the x-axis representing time and the y-axis representing displacement. For each data point, make a point on the graph by corresponding the displacement value along the y-axis and the time value along the x-axis.
Next, draw a straight line that best fits the data points. Ensure that the line passes through most of the points and represents the trend of the data. The slope of this line will give us the speed of the ball.
To find the slope of the line, choose two points on the line (let's call them Point 1 and Point 2). Calculate the change in displacement and divide it by the change in time between these two points. Mathematically, the slope (speed) is given by:
Speed = (Displacement 2 - Displacement 1) / (Time 2 - Time 1)
Choose any two points on the line and plug in their displacement and time values into the formula to calculate the speed. Remember to use consistent units for displacement and time (e.g., centimeters and seconds).
For example, let's choose Point 1 (2.90 cm, 0.60 s) and Point 2 (7.40 cm, 2.10 s):
Speed = (7.40 cm - 2.90 cm) / (2.10 s - 0.60 s)
Speed = 4.50 cm / 1.50 s
Speed = 3.00 cm/s
Repeat this calculation for any other pair of points to verify if the speed remains approximately constant or if it varies.
By analyzing the graph and calculating the slope, we can determine the relationship between displacement and time for the ball rolling along the track.