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Question

The acceleration (a) of a body moving along x-axis is given by a=4x³ ,where a is in m/s² and x is in metre.if at x=0 the velocity of body is 2m/s,then find its velocity at x=4m?

Joshi sir comment

a = 4x³

so dv/dt = 4x³

or dv/dx * dx/dt = 4x³

or dv/dx * v = 4x³

or vdv = 4x³dx

or ∫vdv = 4∫x³dx

or v²/2 = 4x⁴/4 + C

at x = 0, v = 2

so 4/2 = 0+C

so C = 2

on putting the value of C

we get v²/2 = x⁴+ C

now put x = 4 and get v

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