Question

A physics student plots results of an experiment as \(v\) versus \(t .\) The equation that describes the line is given by \(a t=v-v_{0} .\) (a) What is the slope of this line? (b) What is the vertical axis intercept of this line?

Short answer

Question: Determine the slope and vertical axis intercept of the line based on the equation at = v - v_0. Answer: The slope of the line is a, and the vertical axis intercept is v_0.

Step-by-step solution

Rearrange the given equation into slope-intercept form

Rearrange the equation \(at = v - v_0\) as follows: 1. Add \(v_0\) to both sides: \(at + v_0 = v\) 2. Swap left and right sides: \(v = at + v_0\) Now, the equation is in slope-intercept form (\(y=mx+c\)) with \(v\) as dependent variable and \(t\) as independent variable.

Identify the slope and vertical intercept

In the slope-intercept form, compare the coefficients of variables to identify the slope and vertical intercept. With \(v = at + v_0\), the slope (m) corresponds to the coefficient of \(t\), which is \(a\). Thus, the slope of the line is \(a\). The vertical intercept (c) corresponds to the constant term, which is \(v_0\). Thus, the vertical axis intercept of the line is \(v_0\).

Conclusion

The slope of the line in this experiment is \(a\) and the vertical axis intercept is \(v_0\).