How to do convolution related problems?
HINT

The transfer function in the s-domain (using Laplace transform) is given by:

$$\mathcal{H}\left(\text{s}\right):=\frac{\text{v}_\text{o}\left(\text{s}\right)}{\text{v}_\text{i}\left(\text{s}\right)}=\frac{\text{R}}{\text{R}+\text{sL}}\tag1$$

Using the definition of the Laplace transform we know:

$$\text{v}_\text{i}\left(\text{s}\right)=\mathcal{L}_t\left[\text{V}_\text{i}\left(t\right)\right]_{\left(\text{s}\right)}=\int_0^\infty\text{V}_\text{i}\left(t\right)\exp\left(-\text{s}t\right)\space\text{d}t=$$
$$\int_0^1\left(\theta\left(t\right)-\theta\left(t-1\right)\right)\exp\left(-\text{s}t\right)\space\text{d}t\tag2$$

Where \$\theta\left(t\right)\$ is the Heaviside Theta function.



Besides that, an impulse response of a system is given by the output of a system when a Dirac delta function is applied to the input.