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The acceleration of a given particle is given by $a(t) = e^{t/2} - 1$, where $v_0 = 2 m/s$ and $x_0 = 1 m$.

How much time does it take for the particle to reach $x = 50 m$?

Note: this problem involves rather difficult calculus.

$3.8 s$

$4.0 s$

$5.6 s$

$5.7 s$

$9.1 s$