The first thing to do is to calculate the acceleration of the train. We do that by using the acceleration formula, which states
a=(u-v)/t, where a is the acceleration, v is the initial velocity in m/s, u is the final velocity in m/s and t is the time taken in seconds. Looking at our question, we see that t=7.94, u=12.3864 and v=0 (since the train starts from rest). Plug these into the formula, and we get
a=(12.3864-0)/7.94
a=12.3864/7.94
a=39/25=1.56ms^-2
The last thing to do is to calculate the distance travelled. To do that we use this formula (which works with displacement as long as the displacement = distance, as it does in this question):
s=ut+ (at^2)/2, where s is the distance or displacement in metres, u is the initial velocity in m/s, t is the time in seconds and a is the acceleration in m/s^2. Looking at our equation, we see that t=5.57388, u=0 and a=1.54. Plug these into our equation to get
s=0*5.57388 +(1.56*5.57388^2)/2
s=(1.56*5.57388^2)/2
s=48.46629568/2
s~~24.233m, the total displacement of the train.
http://www.dummies.com/education/science/physics/how-to-calculate-time-and-distance-from-acceleration-and-velocity/
I hope I helped!
