A body of mass m starts moving so that it's velocity changes according to the equation v=k√s where k is a constant and s is the displacement.
Find the work done by the force in moving the body in the first t seconds.
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Explanation:
A body of mass m starts moving so that it's velocity changes according to the equation v=k√s where k is a constant and s is the displacement.
Find the work done by the force in moving the body in the first t seconds.
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
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