A particle moves along a straight line such that its displacement at any time t is given by
$s = t^{3} - 6 t^{2} + 3 t + 4$
The velocity when its acceleration is zero, is

Question

A particle moves along a straight line such that its displacement at any time t is given bys $$=$$ $$t3-6t2+3t+4The$$ velocity when its acceleration is zero, is

Infinity Learn · Accepted Answer

x $$=$$ $$t3-6t2+3t+4Velocity$$ v $$=$$ $$dxdt=$$ $$3t2-6$$×$$2t+3$$×$$1+0$$                     $$=$$ $$3t2-12t+3Acceleration$$ a $$=$$ dvdt $$=$$ $$3$$×$$2t$$ $$-12$$×$$1+0$$ $$=$$ $$6t-12Acceleration$$ is zero at time t given by $$6t-12$$ $$=$$ $$0$$⇒ t $$=$$ $$2$$ secondsSo, velocity v at t $$=$$ $$2$$ seconds isv $$=$$ $$(3t2-12t+3)t$$ $$=$$ $$2s$$   $$=$$ $$3$$ ×$$(2)2-12$$×$$2+3$$ $$=-9$$ $$m/s$$

A particle moves along a straight line such that its displacement at any time t is given by
$s = t^{3} - 6 t^{2} + 3 t + 4$
The velocity when its acceleration is zero, is

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A particle moves along a straight line such that its displacement at any time t is given bys = t3-6t2+3t+4The velocity when its acceleration is zero, is

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Ready to Test Your Skills?

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A particle moves along a straight line such that its displacement at any time t is given by
$s = t^{3} - 6 t^{2} + 3 t + 4$
The velocity when its acceleration is zero, is