Q: How do you know when to use this equation as opposed to the other equation for the previous problem for time to accelerate?

A: The equations are really the same if you understand the relatedness of distance (x), velocity (v), time (t), and acceleration (a). Please see the attached diagram. If you have taken calculus it will be easier to understand and you won't have to memorize any formula. Distance (Δx) is the area under the velocity line where it goes from v=0 to v at time t. In calculus, we say distance is the integral of v over time. Acceleration (a) is the slope of the graph. In calculus, we say acceleration is the derivative of velocity. Note that these problems assume constant acceleration (linear slope), which make them simple to solve and appropriate for tests with limited duration such as MCAT.