TOTAL FOR SECTION A IS 50 MARKS SECTION B: MECHANICS Answer ALL questions. Unless otherwise indicated, whenever a numerical value of is required, take = 9.8 m s–2 g g and give your answer to either 2 significant figures or 3 significant figures. At time seconds, where 0, a particle moves so that its acceleration m s2 is given by 6. a t t P a = 5t i j – When = 0, the velocity of is 20i m s1 t P Find the speed of when = 4 P t (Total for Question 6 is 6 marks) ___________________________________________________________________________ 7. A rough plane is inclined to the horizontal at an angle where tan 𝛼, 𝛼 A particle of mass is placed on the plane and then projected up a line of greatest slope of m the plane. The coefficient of friction between the particle and the plane is µ. The particle moves up the plane with a constant deceleration of g (a) Find the value of µ. (6) The particle comes to rest at the point on the plane. A (b) Determine whether the particle will remain at carefully justifying your answer. A, (2) (Total for Question 7 is 8 marks) ___________________________________________________________________________ 8. [In i j this question and are horizontal unit vectors due east and due north respectively.] A radio controlled model boat is placed on the surface of a large pond. The boat is modelled as a particle. At time = 0, the boat is at the fixed point and is moving due north with speed 0.6 m s1. t O
TOTAL FOR SECTION A IS 50 MARKS SECTION B: MECHANICS Answer ALL questions. Unless otherwise indicated, whenever a numerical value of g is required, take g = 9.8 m s–2 and give your answer to either 2 significant figures or 3 significant figures. 6. At time t seconds, where t 0, a particle P moves so that its acceleration a m s2 is given by a = 5t i – j When t = 0, the velocity of P is 20i m s1 Find the speed of P when t = 4 (Total for Question 6 is 6 marks) ___________________________________________________________________________ 7. A rough plane is inclined to the horizontal at an angle 𝛼, where tan 𝛼 A particle of mass m is placed on the plane and then projected up a line of greatest slope of the plane. The coefficient of friction between the particle and the plane is µ. The particle moves up the plane with a constant deceleration of g (a) Find the value of µ. (6) The particle comes to rest at the point A on the plane. (b) Determine whether the particle will remain at A, carefully justifying your answer. (2) (Total for Question 7 is 8 marks) ___________________________________________________________________________ 8. [In this question i and j are horizontal unit vectors due east and due north respectively.] A radio controlled model boat is placed on the surface of a large pond. The boat is modelled as a particle. At time t = 0, the boat is at the fixed point O and is moving due north with speed 0.6 m s1.
03a_a_level_mathematics_sams_-_paper_3_statistics_and_mechanics.docx