SPM 2022 Add Maths Paper 2, Question 15Kinematics of Linear Motion

Solved on video in English and Bahasa Melayu · 10 marks · Form 5, Kinematics of Linear Motion · 4:51 video

The question

(a)

Solution by graph sketching is not accepted. Diagram 7 shows two particles, A and B, moving along a straight line. At instant t = 0, particle A and particle B move off from point M and point N respectively. The displacement, s m, from point M for particle A and from point N for particle B is given by s_A = t³ + 4t² + 5t and s_B = t³ − t² + 4t + 18, such that t is time, in seconds.

(a) Find the initial velocity, in m s⁻¹, of particle A and particle B.

[3 marks]

(b)

Using s_A = t³ + 4t² + 5t and s_B = t³ − t² + 4t + 18:

(b) Find the distance, in m, travelled by particle A and particle B at the instant they collide.

[4 marks]

(c)

Using v_A = 3t² + 8t + 5 and v_B = 3t² − 2t + 4, with collision at t = 1.8 s:

(c) Calculate the acceleration, in m s⁻², for particle A and particle B immediately before the collision occurs.

[3 marks]

SPM 2022 Add Maths Paper 2, Question 15: the question as drawn in Eduly's video4:51

Part (a)

Step 1

Velocity is the derivative of displacement with respect to time.

Why this step

Displacement says where the particle is; velocity is how fast that changes. So differentiate first. Do not put t = 0 into s.

5 more steps, each with the reason for it, in the full solution

Final answer

A = 5 m s⁻¹, B = 4 m s⁻¹

Where students lose marks

Watch out: differentiate s to get v before putting t = 0. Substituting t = 0 into s only gives the starting position.

Part (b)

11 more steps, each with the reason for it, in the full solution

Final answer

A = 27.792 m, B = 9.792 m

Where students lose marks

Watch out: B did not start at M. Subtract its starting displacement, 18, from s_B(1.8), otherwise you wrongly get 27.792 m for B.

Part (c)

6 more steps, each with the reason for it, in the full solution

Final answer

A = 18.8 m s⁻², B = 8.8 m s⁻²

Where students lose marks

Watch out: substitute the collision time t = 1.8 s, not the distance 27.792, into your acceleration functions.

Watch every step of this question solved on video (4:51), with the reason behind each step and a box that checks your own answer.

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