When a train is travelling along a straight track at 2 m/s, it begins to accelerate at a = (60v^(-4)) m/s^2, where v is in m/s. Determine its velocity v and its position 3 s after the acceleration.

Question

When a train is travelling along a straight track at 2 m/s, it begins to accelerate at a = (60v^(-4)) m/s^2, where v is in m/s.  Determine its velocity v and its position 3 s after the acceleration.

lastdaywork · Answer

a = 60v^(-4)
dv/dt = 60v^(-4)
$$\int\limits v^4 dv = 60 \int\limits dt + C$$
You can calculate C by using v = 2 at t = 0

Similarly find distance as a function of time.
Finally put t = 3 to get the corresponding velocity and position.

anonymous · Answer

Thanks!  It's actually quite easy!

lastdaywork · Answer

You're welcome :)