Question

1. when velocity is graphed with respect to time, what does the area under the line represent? acceleration distance velocity displacement

Explanation:

Velocity is defined as the rate of change of displacement with respect to time. When we graph velocity ($v$) against time ($t$), the area under the curve is calculated as $\int_{t_1}^{t_2}v\mathrm{d}t$. By the fundamental theorem of calculus, since $v=\frac{\mathrm{d}s}{\mathrm{d}t}$ (where $s$ is displacement), then $\int_{t_1}^{t_2}v\mathrm{d}t=\int_{t_1}^{t_2}\frac{\mathrm{d}s}{\mathrm{d}t}\mathrm{d}t=s(t_2)-s(t_1)$, which is the displacement over the time interval $[t_1,t_2]$.

Answer:

displacement