# Rocket speed of light question

A rocket ship in free space moves with constant acceleration 32 ft/sec^2. (a) If it starts from rest, how long will it take to acquire a speed one-tenth that of light? (b) How far will it travel in doing so?

So we are given $a_{x} = 32 \frac{ft}{sec^{2}}$, and $v_{x}_{0} = 0$. One-tenth the speed of light is $1.86\times 10^{4} \frac{miles}{sec}$. For the first part would I use $v_{x} = v_{x}_{0} + a_{x}t$? And for the second part I could use $x = x_{0} + v_{x}_{0}t + \frac{1}{2}a_{x}t^{2}$

Thanks

If the acceleration is measured in $f/s^2$, then your speed must be measured in feet/sec, not miles/sec. (Do the unit conversion.) Other than that, your method looks good.