Question

which equation is most likely used to determine the acceleration from a velocity vs. time graph?
○ $a = \frac{t}{\delta v}$
○ $m = \frac{v_2 - v_1}{x_2 - x_1}$
○ $a = \frac{\delta v}{m}$
○ $m = \frac{x_2 - x_1}{v_2 - v_1}$

Explanation:

Step1: Recall the formula for acceleration

Acceleration \(a=\frac{\Delta v}{\Delta t}\), and on a velocity - time graph, the slope \(m\) of the graph (where \(m = \frac{y_2 - y_1}{x_2 - x_1}\), with \(y\) as velocity \(v\) and \(x\) as time \(t\)) gives the acceleration.

Step2: Analyze each option

• For \(a=\frac{t}{\Delta v}\), this is not the correct formula for acceleration.
• For \(m=\frac{v_2 - v_1}{x_2 - x_1}\), if \(y = v\) (velocity) and \(x=t\) (time), then \(m=\frac{v_2 - v_1}{t_2 - t_1}\), which is the formula for acceleration (\(a=\frac{\Delta v}{\Delta t}\)).
• For \(a=\frac{\Delta v}{m}\), this is not relevant to finding acceleration from a velocity - time graph ( \(m\) here is not defined correctly in the context of the graph).
• For \(m=\frac{x_2 - x_1}{v_2 - v_1}\), this is the reciprocal of the slope formula for acceleration (incorrect).

Answer:

\(m=\frac{v_2 - v_1}{x_2 - x_1}\) (assuming \(y = v\) (velocity) and \(x = t\) (time))