Question

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

Answer 1

The acceleration of the body is determined by differentiating the velocity, and velocity by differentiating the displacement. By doing the reverse, we integrate the acceleration to get the velocity and integrate the velocity to get the displacement.
velocity = 20v^-3 and displacement = (20/3)v^-2
Substituting the value of v,
velocity = 20/(2 m/s)^3 = 2.5 m/s
displacement = 20/3 / (2m/s)² = 5/3 m