explain in words what the integral represents and give units. ∫₀⁹ a(t) dt, where a(t) is acceleration in…

Brief Explanations:

The definite - integral of acceleration with respect to time over an interval gives the change in velocity over that time interval. We know that acceleration $a(t)=\frac{dv}{dt}$, and by the fundamental theorem of calculus, $\int_{t_1}^{t_2}a(t)dt = v(t_2)-v(t_1)$. The units of acceleration are $\text{km/hr}^2$ and the units of time are hours. When we multiply the units of $a(t)$ and $dt$ (units of time), we get $\text{km/hr}^2\times\text{hr}=\text{km/hr}$.

Answer:

The integral represents the change in velocity from $t = 0$ to $t = 9$ hours. The units are km/hr.