Difficult# Time Required to Reach x(t) Given a(t)

APPHMC-PEHEGK

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.