How to Solve a Spaceship Calculus Problem?

[JakePearson]

if a spaceship accelerates, from rest at time t=0, at a rate of 2t / sqrt(1 + t²) ms^-2 at time t, calculate in years to 1 significant figure how long it would take to reach the speed of light 3x10⁸ ms^-1?

i got an answer of 5 years, is this correct, but i have made a mess of my workings, what is the best way to answer this question in the shortest time period?

many thanks

 

[Dick]

How did you work it out? It's pretty straightforward, isn't it?

 

[kNYsJakE]

This is a very straight forward problem.

All you need to know is that you get a velocity when you integrate acceleration respect to time.

After that, it's all algebra. plug-in, and solve for t.