Units for the Integral of a Velocity Function

Question

What would be the units for the integral of a velocity function? More specifically the units for this integral:

$$\frac1{12}\int_0^{12}v(t)dt$$

where $v(t)$ is a velocity function in meters per second.

I think it should be in meters, as velocity is the first derivative of displacement. My calc teacher says that this would yield a velocity with meters per second as the unit, as this would be the average value of the function. She says that $\int_0^{12}v(t)$ would yield a displacement (meters as the unit), so I'm confused about how multiplying it by $\frac1{12}$ would change the units.

Answer 1

The limits of integration (0 and 12) have units of seconds (they are values of $t$), so the 1/12 has units of inverse seconds.

Answer 2

The integral does represent the displacement. I believe that $\frac1{12}$ is not just a constant, however; I believe the fraction represents $\frac1{12\text{ seconds}}$ which would explain why the units is meters/second.

Answer 3

You're integrating differential displacements, given by the products of instantaneous velocities and differential times. Thus the integral is also a displacement.