Question

In the following math question:
The position, x metres, of a particle travelling in a straight line from a fixed origin at time t seconds is given by x (t) = 3t^3 - 9t^2 + 12t - 2, 0 ≤ t ≤ 3.
Determine, correct to 2 decimal places, the time(s) when the numerical component of the particle’s velocity and the numerical component of the acceleration are equal.

What does it mean when the question says "numerical component"?

Answer 1

When the question refers to the "numerical component" of the particle's velocity and acceleration, it means to consider only the magnitude or absolute value of the velocity and acceleration without considering their direction. Essentially, we are looking for when the speed of the particle (the absolute value of the velocity) is equal to the magnitude of the acceleration.