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# calc question?

A particle moves along a straight line with the equation of motion s= t^6-2t^5 Find the value of t (other than 0 ) at which the acceleration is equal to zero.

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- ?Lv 71 month ago
s(t) = t⁶ - 2t⁵

v(t) = ds(t)/dt = 6t⁵ - 10t⁴

a(t) = dv(t)/dt = 30t⁴ - 40t³

a(t) = t³(30t - 40) = 0

t³ = 0 → t = 0 (multiplicity = 3)

30t - 40 = 0 → t = 4/3

Ans: Acceleration is zero at t = 0 and t = 4/3

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