A particle moves along the x-axis so that at time t > (or equal to) 0 its position is given by x (t) = 2t^3 - 21t^2 + 72t-53. At what time t is the particle at rest? ... ?

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Physics

Milo

13 March, 17:19

A particle moves along the x-axis so that at time t > (or equal to) 0 its position is given by x (t) = 2t^3 - 21t^2 + 72t-53. At what time t is the particle at rest? ... ?

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Duckling · Answer 1

Particle is at rest when Velocity = 0

V = X ' (t) = 6t^2 - 42t + 72 = 0

V = t^2 - 7t + 12 = 0

Solve for t:t1 = 3t2 = 4Particle is at rest at t = 3 and t = 4.