A particle moves along the x-axis so that at time t\ge 0t≥0 its position is given by x(t)=-2t^3+42t^2.x(t)=−2t 3 +42t 2 . Determine all intervals when the particle is moving to the right.

Question

A 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.

Answer 1

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