Paper 2 Section C Practice

Kinematics of Linear Motion • 10-Mark Mastery

SPM Paper 2 Section C Specialty

Form 5 Chapter 8: Kinematics of Linear Motion

Total Marks: 40 Marks • Time Allowed: 50 Minutes

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A Bahagian A: Calculus Linkage Drills [10 Marks]

Answer all questions
Soalan 1 [5 Marks]

A particle moves along a straight line with a velocity of $v = 3t^2 - 12t + 9\text{ ms}^{-1}$, where $t$ is the time in seconds after starting from a fixed origin $O$.

(a) Find the initial acceleration of the particle. [2 marks]

(b) Find the values of $t$ when the particle reverses its direction of motion. [2 marks]

(c) State the range of values of $t$ for which the velocity is decreasing. [1 mark]

Soalan 2 [5 Marks]

A particle passes through a fixed point $O$ with velocity $8\text{ ms}^{-1}$. Its acceleration is given by $a = 4 - 2t\text{ ms}^{-2}$. Find the displacement $s$ of the particle from $O$ when its velocity is maximum.

B Bahagian B: SPM Paper 2 Section C Full Blueprint [20 Marks]

Answer both 10-mark questions
Soalan 3 (Paper 2 Section C Model) [10 Marks]

A particle moves along a straight line and passes a fixed point $O$. Its velocity $v\text{ ms}^{-1}$ is given by $v = 2t^2 - 10t + 8$, where $t$ is the time in seconds after passing $O$. [Assume motion to the right is positive]

(a) Find the initial velocity of the particle. [1 mark]

(b) Calculate the minimum velocity of the particle. [3 marks]

(c) Find the values of $t$ when the particle is instantaneously at rest. [2 marks]

(d) Calculate the total distance, in $\text{m}$, travelled by the particle in the first $4$ seconds after leaving $O$. [4 marks]

Soalan 4 (KBAT Autonomous Electric Vehicle Braking) [10 Marks]
An autonomous electric vehicle (EV) is undergoing highway obstacle detection testing. The EV travels at a cruising velocity of $30\text{ ms}^{-1}$ when its LiDAR sensor detects a stationary obstacle at $t = 0$. The on-board emergency braking system initiates a deceleration $a\text{ ms}^{-2}$ modeled by:
$a(t) = -2t - 4, \quad t \ge 0$
where $t$ is the time in seconds after the braking sequence begins.

(a) Show that the velocity of the vehicle during the braking sequence is given by $v(t) = 30 - 4t - t^2$. [2 marks]

(b) Determine the time taken, in seconds, for the autonomous vehicle to come to a complete stop. [3 marks]

(c) Calculate the stopping distance of the vehicle from the moment the brakes were engaged. [3 marks]

(d) If the obstacle was initially detected at a distance of $65\text{ meters}$ ahead and the vehicle had a sensor-to-actuator reaction delay of $0.4\text{ seconds}$ before the brakes engaged, determine whether the autonomous EV will collide with the obstacle. Justify your answer. [2 marks]