[tex]a=5000\dfrac{mm}{s}=5\dfrac{m}{s}[/tex]
[tex]f=10{Hz}\Longrightarrow t=\dfrac{1}{10}s[/tex]
[tex]a_{max}=\dfrac{50\frac{m}{s}}{\frac{s}{10}}\cdot\dfrac{1}{\sqrt{2}}=\dfrac{50\dfrac{m}{s^2}}{\sqrt{2}}\approx\boxed{35.4\dfrac{m}{s^2}}
[/tex]
Hope this helps.
r3t40
