How do I solve this LTI acceleration sensor problem?

[Nikitin]

Homework Statement

Please see he attached file for the problem text.

Homework Equations

The output $y(t) = h(t) * x(t)$, where $h(t)$ is the system's impulse response while $x(t)$ is the input signal.

Laplace transformed, the formula above turns into $Y(s)=H(s) \cdot X(s)$, where $H(s)$ is the transfer function.

The Attempt at a Solution

Uhm, well.. I am very lost.

1) Why does the transfer function have units Volt/Acceleration ? Isn't it the impulse response that should have those units?

2) Why exactly does a laplace-transform of a signal move the signal to the frequency domain? Is it just because the new variable has units 1/Second ?

Anyway, to solve this problem I know that $X(s)=a_0/s$, since $x(t) = a_0 u(t)$, with $u(t)$ being the unit-step function. But how do I proceed?

 

[Nikitin]

Guys the problem is solved. no need to answer