How do you do this?

Question

You re driving parallel to train tracks at 65.0 km/h when a train passes you, going a steady 96.0 km/h. A track crossing is up ahead, so you begin to speed up at 8.00 m/s^2. How far do you drive before you pass the train?

Answer 1

u = speed of train = 96 km/h  [constant]

 

v = your initial speed at instant the train passes you = 65 km/h

 

a = your constant acceleration (which began at time t=0) = 8 m/s²

 

t = time when you reach the train, with t=0 set at the moment when the train passed you

 

x = distance you travel when you reach the train at time t, with x=0 set at where the train passed you

 

Both the train and you travel the same distance x.

 

Train:

 

x = ut

 

You:

 

x = vt + at²/2

 

Then

 

ut = vt + at²/2

 

at²/2 + (v - u)t = 0

 

t[at/2 + (v - u)] = 0

 

t = 2(u - v)/a

 

Plug in the numbers for u, v, and a in compatible units and get t.  Then plug t into either

 

x = ut

 

or

 

x = vt + at²/2

 

to get x.  Be careful with the units.  You should be able to finish from here.