# A body starts from origin moves along the x axis such that the velocity at any instant is given by( 4t^3-2t) .what is the acceleration of the particle when it is at a distance 2 meter from the origin?

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by bristy

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by bristy

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a = dv/dt = 12t² - 2 ---------------------------(1)

ds/dt = v = 4t³ - 2t

ds = (4t³ - 2t)dt

integrate both side limit of s is 0 to 2 & limit of t is 0 to t

2 = t^4 - t²

t^4 - 2t² + t² - 2 = 0

t²(t² - 2) + 1(t² - 2) = 0

(t² + 1)(t² - 2) = 0

t² - 2 = 0

t = √2 (as time can not be negative so left t = -√2)

t² + 1 = 0 (never zero)

put t = √2 in equation (1)

a = 24 - 2

a = 22 m/s²