Question

A locomotive of mass m starts with a velocity = ax (1/2) where a is constant and root of x. Find the work done by all the forces acting on locolocomotive in first t seconds .
Ans is m(a) (raise to power 4)t square upon 8

Plz help me its urgent
Pl explain whole

Answer 1

v = a√x
dx/dt = a√x
dx / (a√x) = dt
1/a × dx / (√x) = dt
Integrating x with limits 0 to x and dt from 0 to t
2√x / a = t
x = (at / 2)²
Displacement = (at / 2)²

Acceleration = vdv/dx
= a√x d(a√x)/dx
= a²√x × (0.5) × 1/√x
= a²/2

W = Force × Displacement
= Mass × acceleration × Displacement
= m × (a²/2) × (at/ 2)²
= (ma²/2) × (a² t²/ 4)
= ma⁴ t² / 8

Answer 2

see the attachment for the answer