# Units after integrating a ratio metric: Point Source Transfer Mobility

I want to calculate the so called Line Source Transfer Mobility (LSTM) from 10 equispaced Point Source Transfer Mobilities (PSTM).

The PSTM measures the response to an excitation, and it is defined as velocity / force, so the units are [(m/s)/N].

The LSTM is obtained through integration over the different equispaced PSTMs.

I am trying to understand why the resulting units of the LSTM (as shown in several bibliogaphic references) are [(m/s)*sqrt(m)/N].

At first I thought, okey, easy, the units will be [(m/s)*(m)/N], since I am integrating over distance (ds). But then I saw the [sqrt(m)] and I did not understand anything.

I believe it might have to do with the fact that, even though the 10 impacts are performed at different locations (thus the integration over the distance covered by the 10 different impact locations), the velocity (the response) is always measured at one same location. But this could also not have anything to do with it, just saying in case it fosters some inspiration.