The particle is moving in the direction of velocity. So the answer to the question would be when the velocity (derivative of position) is >0

V=x'=-6t^2 + 84t > 0

Solving inequality (factoring out - 6t):

-6t (t - 14) > 0

It is positive from 0 to 14

Kristen K.

asked • 13dA particle moves along the *x*-axis so that at time t≥0 its position is given by x(t)=−2t3+42t2. Determine all intervals when the particle is moving to the right.

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The particle is moving in the direction of velocity. So the answer to the question would be when the velocity (derivative of position) is >0

V=x'=-6t^2 + 84t > 0

Solving inequality (factoring out - 6t):

-6t (t - 14) > 0

It is positive from 0 to 14

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