8. The image set interval of the interval $[0, m]$ under the mapping $f: x \rightarrow 2 x+m$ is $[a, b]$. If the length of the interval $[a, b]$ is 5 units greater than the length of the interval $[0, m]$, then $m=(\quad)$.
(A) 5
(B) 10
(C) 2.5
(D) 1
8. A.

The length of the interval $[0, m]$ is $m$. Under the mapping $f$, the corresponding image set interval is $[m, 3m]$, with an interval length of $2m$. Therefore, $m=2m-m=5$.