In an experiment, two variables quantities 'x' and 'y' were measure. The relation between x and y is thought to be y=ax^(1/2)
x(m)+/- 0.01m
0.10
0.20
0.40
0.80
1.00
y(s) +/- 0.05s
0.64
0.90
1.27
1.80
1.90
a) What will you graph in the y- and x- axis in order to obtain a straight line graph?
b) Draw and complete a table which allows you yo plot the graph(what is missing to draw an additional table??)
c) Explain why under certain circumstances the graph may not pass through the origin?
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please check and correct
a) in the x-axis i will have the sqrt'x' and the y-axis the 'y' variable
b) i make a table with the value of sqrt of 'x' and the given y values
c) just plot the points but how do i find the constant, i tried it algebraically i got 1.02 for the first row and second row onwards 1.01.
d)inaccuracies of experiment is one of the reasons why it may not pass the origin, but it has something to do with the sqrt and the power law right?
a) In order to obtain a straight line graph, you should graph y on the y-axis and the square root of x on the x-axis. This is because according to the given relation, y is proportional to the square root of x.
b) To complete the table and plot the graph, you need to calculate the square root of each x value. Here is the completed table:
x(m) +/- 0.01m | √x | y(s) +/- 0.05s
----------------------------------------------
0.10 | 0.316 | 0.64
0.20 | 0.447 | 0.90
0.40 | 0.632 | 1.27
0.80 | 0.894 | 1.80
1.00 | 1.000 | 1.90
c) The graph may not pass through the origin under certain circumstances because the relationship in the given equation does not necessarily imply that y will be zero when x is zero. This is because the initial equation, y = a * x^(1/2), does not have a constant term (y-intercept) and is only proportional to the square root of x. In practical situations, it is possible that the y-axis intercept may not be at zero due to other factors or errors in measurement.