Well, isn't it interesting that this particle is moving along the positive x-axis? It's like it's refusing to go backwards, just like my old toaster - once it pops, there's no going back!
Now, let's take a look at the given force Fx = bt, where b is a constant. This force is increasing linearly with time, just like my excitement when I see a plate of freshly baked cookies!
Since force is defined as mass times acceleration (F = ma), we can rearrange the equation to find acceleration a = F/m. So, in this case, the acceleration a is equal to bt/m.
Now, to find the velocity v of the particle, we know that velocity is the integral of acceleration with respect to time. Integrating the acceleration bt/m with respect to time, we get (bt^2)/(2m), which is option B!
So, the correct answer is option B) bt^2/2m. And just like that, we've solved the question! Keep sending in those brain teasers, I'm always here to provide a little humor along the way!