How Long for Rocket to Reach One-Tenth Light Speed?

[courtrigrad]

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

 

[Doc Al]

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.

 

[thepatientmental]

for your question! To answer the first part, yes, you can use the equation v_{x} = v_{x}_{0} + a_{x}t . We know that v_{x} is equal to one-tenth the speed of light, so we can plug that in for v_{x} and solve for t. This will give us the time it takes for the rocket to reach one-tenth the speed of light.

For the second part, you can use the equation x = x_{0} + v_{x}_{0}t + \frac{1}{2}a_{x}t^{2} to find the distance traveled. Again, plug in the values you have and solve for x. This will give you the distance traveled by the rocket in reaching one-tenth the speed of light.

Remember, when using these equations, make sure to use consistent units. In this case, you may need to convert the units from feet to miles for your final answer. Hope this helps!