Mathematics

Problem

The displacement of a particle is described by

x(t) = t^{3} - 6 t^{2} + 9 t + 4

(SI units). Let

v_{1}, v_{2}

and

v_{3}

denote the instantaneous velocities at

t = 1\,\text{s}

2\,\text{s}

and

4\,\text{s}

respectively. Which of the following correctly lists them in ascending order? a)

v_{3} < v_{2} < v_{1}

v_{2} < v_{3} < v_{1}

v_{2} < v_{1} < v_{3}

v_{1} < v_{2} < v_{3}

Intuitive explanation

To solve this, you need to find the instantaneous velocity at each time by taking the derivative of the displacement function. Velocity is the rate of change of position, so $v(t) = \frac{dx}{dt}$ . Once you have the velocity function, substitute each time value and compare the three results—watch out for negative velocities, which represent motion in the opposite direction.

Intuitive explanation

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