csat-suneung 2025 Q11

csat-suneung · South-Korea · csat__math 4 marks Applied differentiation Kinematics via differentiation
A point P starts at time $t = 0$ and moves on a number line. At time $t$ ($t \geq 0$), its position $x$ is given by $$x = t^{3} - \frac{3}{2}t^{2} - 6t$$ What is the acceleration of point P at the time when its direction of motion changes after starting? [4 points]
(1) 6
(2) 9
(3) 12
(4) 15
(5) 18
A point P starts at time $t = 0$ and moves on a number line. At time $t$ ($t \geq 0$), its position $x$ is given by
$$x = t^{3} - \frac{3}{2}t^{2} - 6t$$
What is the acceleration of point P at the time when its direction of motion changes after starting? [4 points]\\
(1) 6\\
(2) 9\\
(3) 12\\
(4) 15\\
(5) 18