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 y(s) +/- 0.05s
0.10 0.64
0.20 0.90
0.40 1.27
0.80 1.80
1.00 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?
a) In order to obtain a straight line graph, we need to manipulate the equation y = ax^(1/2) to have a linear form. To do this, we can take the square of both sides of the equation, which gives us y^2 = a^2x. Now we have a linear relationship between y^2 and x. Therefore, we will graph y^2 on the y-axis and x on the x-axis to obtain a straight line graph.
b) To draw the graph, we need to complete a table that includes the values of y^2 corresponding to the given x values. We can calculate the values of y^2 by squaring the y values given in the question. The completed table will look as follows:
x(m) +/- 0.01m y(s) +/- 0.05s y^2(s^2)
0.10 0.64 0.4096
0.20 0.90 0.8100
0.40 1.27 1.6129
0.80 1.80 3.2400
1.00 1.90 3.6100
c) The graph may not always pass through the origin (0,0) if there is an offset or non-zero intercept in the relationship between x and y. In this particular case, the equation y = ax^(1/2) does not pass through the origin because the square root function does not have a value when x = 0. Therefore, the graph starts at a non-zero value of y when x is zero. This can be understood by observing that when x = 0, y = 0^(1/2) = undefined. Additionally, if there are other factors influencing the relationship between x and y, such as measurement errors or experimental conditions, the graph may deviate from passing through the origin.