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A particle moves in a straight line and t seconds after passing a fixed point O, its velocity is (3t2-4t) m/s Calculate (a)its velocity when its acceleration is zero (b)its distance from O when its velocity is zero again.

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A particle moves in a straight line and t seconds after passing a fixed point O, its velocity is (3t2-4t) m/s Calculate (a)its velocity when its acceleration is zero when its velocity is (3t2-4t), its acceleration will be A=d/dt(3t2-4t) =6t-4 put A=0 0=6t-4 t=2/3 then its velocity is 3(2/3)2-4(2/3) =-4/3 its velocity is 4/3 m/s in the opposite direction of its motion (b)its distance from O when its velocity is zero again. ∫(3t2-4t)dt displacement D= t^3 -2t^2 C when t=0, D=0, so D= t^3 -2t^2 when its velocity is zero again, put v=0 0=3t2-4t t=0 or 4/3 put t=4/3 D=(4/3)^3 -2(4/3)^2 D=-32/27 its distance from O is 32/27 m

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