The position function of a particle is given by:
The velocity function is the derivative of the position:
The particle will be at rest when the velocity is 0, thus we solve the equation:
The coefficients of this equation are: a = 2, b = -9, c = -18
Solve by using the formula:
Substituting:
We have two possible answers:
We only accept the positive answer because the time cannot be negative.
Now calculate the position for t = 6:
