A simple pendulum is suspended from the roof of a car. The car...

Let the acceleration of the car be $a$.

In the non-inertial frame of the car, a pseudo force $ma$ acts on the pendulum bob in the backward direction, while gravity $mg$ acts downwards.

At equilibrium, the angle $\theta$ made by the string with the vertical is given by:
$\tan \theta = \dfrac{ma}{mg} = \dfrac{a}{g}$

Given that $\theta = \tan^{-1}(0.5)$, we have:
$\dfrac{a}{g} = 0.5 \Rightarrow a = 0.5g$

Using the first equation of motion for the car starting from rest ($u = 0$):
$v = u + at$
$v = 0 + (0.5g)t = 0.5gt$

Answer: $0.5gt$