To determine the acceleration from a velocity vs. time graph, you need to understand the relationship between velocity, time, and acceleration. Acceleration [tex]\( a \)[/tex] is defined as the change in velocity ([tex]\( \Delta v \)[/tex]) divided by the change in time ([tex]\( \Delta t \)[/tex]).
This can be expressed using the equation:
[tex]\[ a = \frac{\Delta v}{\Delta t} \][/tex]
However, this specific equation is not among the provided options. Instead, we can find the relevant concept related to this relationship. The acceleration can also be understood as the slope of the velocity vs. time graph. The slope formula in general terms is:
[tex]\[ m = \frac{y_2 - y_1}{x_2 - x_1} \][/tex]
In the context of a velocity vs. time graph, the slope (m) would represent the acceleration (a), as it shows the rate of change of velocity with respect to time.
Replacing [tex]\( y_2 - y_1 \)[/tex] with [tex]\( \Delta v \)[/tex] (change in velocity) and [tex]\( x_2 - x_1 \)[/tex] with [tex]\( \Delta t \)[/tex] (change in time), the formula becomes:
[tex]\[ a = \frac{v_2 - v_1}{t_2 - t_1} \][/tex]
Thus, the relevant approach to find acceleration from a velocity vs. time graph is determined by identifying the slope of the graph, and the correct equation related to the context given in the options is:
[tex]\[ m = \frac{y_2 - y_1}{x_2 - x_1} \][/tex]
So, the most likely used equation for determining the acceleration from a velocity vs. time graph is:
[tex]\[ m = \frac{y_2 - y_1}{x_2 - x_1} \][/tex]
This corresponds to option 2.
