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AP® Physics C: Mechanics

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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.

A

$3.8 s$

B

$4.0 s$

C

$5.6 s$

D

$5.7 s$

E

$9.1 s$