Question

if you were to find the area under a velocity - time graph, which of the following quantities would you be calculating? (a) displacement (b) instantaneous velocity (c) average acceleration (d) time

Explanation:

In a velocity - time graph, the area under the graph is calculated by integrating velocity with respect to time (or using geometric formulas for simple graphs like rectangles, triangles). The formula for displacement ($s$) is given by the integral of velocity ($v$) with respect to time ($t$), i.e., $s=\int v\mathrm{d}t$. This integral represents the area under the velocity - time curve. Instantaneous velocity is just the value of the velocity at a particular time (the y - value on the graph), average acceleration is the change in velocity over change in time (slope of the velocity - time graph), and time is the x - axis variable, not the area under the graph. So the area under the velocity - time graph gives displacement.

Answer:

a. displacement