You're driving parallel to train tracks at 52.0 km/h when a train passes you, going a steady 91.0 km/h. A track crossing is up ahead, so you begin to speed up at 8.00 m/s2. How far do you drive before you pass the train?

Answer 1

8.0 m/s^2 * 1km/1000m * (3600s/hr)^2 = 103680 km/hr^2

after h hours, the distances must be the same:

91.0h = 52.0h + 51840h^2
h = 0.000752315 hours = 2.7 seconds

Or, you may want to convert km/hr to m/s, but the answer is the same.

To get the distance, just plug it into either side of the equation.

That seems pretty fast to catch up, but 8.0 m/s^2 = 28.8 km/hr/s, so after 2.7 seconds, you have accelerated to 52+28.8*2.7=129.76 km/hr, so I guess the time seems reasonable, yeah?