SPM 2024 Add Maths Paper 2, Question 14Kinematics of Linear Motion

Solution by graph sketching is not accepted.

Particle P moves along a straight line such that fixed points A and B lie on the straight line. Its velocity, in m s⁻¹, is given by v = 3t² + 4t − 15, such that t is the time, in seconds, after passing through point A towards point B.

[Assume motion to the right is positive.]

(a) Determine whether point A is to the left or to the right of point B. Justify your answer.

Determine whether point A is to the left or to the right of point B. Justify your answer.

(b) Find the acceleration, in m s⁻², of the particle at t = 1.3 s.

Find the acceleration, in m s⁻², of the particle at t = 1.3 s.

(c) If the distance between points A and B is 15 m, determine whether the particle will pass point B or not. Give a reason for your answer. [4 marks]

If the distance between points A and B is 15 m, determine whether the particle will pass point B or not. Give a reason for your answer. [4 marks]

(d) Particle Q moves along the same straight line such that its velocity, v m s⁻¹, is given by v = 2t² − 7t + 6, such that t is the time, in seconds, after passing through point A.

Determine the range of time, in seconds, when both particles move to the left.

Particle Q moves along the same straight line such that its velocity, v m s⁻¹, is given by v = 2t² − 7t + 6, such that t is the time, in seconds, after passing through point A.

Determine the range of time, in seconds, when both particles move to the left.