The position of a particle is given by S(t) = t^3 - 6t^2 + 2 when does the particle change direction?Step by step process

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justaguide | College Teacher | (Level 2) Distinguished Educator

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The particle is moving such that its position is given by S(t) = t^3 - 6t^2 + 2.

When the particle changes direction the velocity changes sign.

Velocity is given by V(t) = S'(t) = 3t^2 - 12t

3t^2 - 12t = 0

=> 3t = 12

=> t = 12/3

=> t = 4

Before t = 4, the velocity of the particle is negative, after t = 4 the velocity of the particle becomes positive.

At t = 4, the particle changes direction.

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