Please solve these 5 Alevel Maths questions as quickly as you can, easy step by step on a piece of paper...(with clear diagrams and labels)! Thank youThe answers are given for the following questions and please work it out to get these answersQuestion 1: (a)0.98 ms-2, (b)18N, (c)... (d)1.3 ms-1, (e)0.51s Question 2: (a) 20 ms-1 (b) 10 ms-2Question 3: (a) r=(2t^4 - 3t^2 -4)i+ (4t^2 -3t -7)j ms-1, (b) t=74Question 4: (a) (-i - 1/4j) ms-1, (b) (94i - 654j) mQuestion 5: (a) v= - (sin4?t/4?), (b) 1/4?, (c) s= (cos4?t/16?^2 - 1/16?^2), (d) 1/8?^2, (e) 16

1. The diagram shows two particles P and Q, of mass 3 kg and 2 kg respectively, connected by a light inextensible string. Initially P is held at rest on a fixed smooth plane inclined at an angle 30 to the horizontal. The string passes over a smooth light pulley A fixed at the top of the plane. The part of the string from P to A is parallel to the line of greatest slope of the plane. The particle Q hangs freely below A. The system is released from rest with the string el a) Find the acceleration of Q R R e R R P (3 ke) @ '(J:'.tk;n B e t 0.8m c) State where in your e . . i calculations you have used the information that the string is inextensible. On release, Q is at a height of 0.8m above the ground. When Q reaches the ground, it is brought to rest immediately by the impact with the ground and does not rebound. The initial distance of P from A is such that in the subsequent motion P does not reach A. 200 d) the speed of Q as it reaches the ground e) the time between the instant when Q reaches the ground and the instant when the string becomes taut again. 2. At time t seconds, a particle P has position vector r m with respect to a fixed origin O, where r=at'i + (24t - 3t")j, 20 a) Find the speed of P whent = 2 b) Show that the acceleration of P is a constant and find the magnitude of this acceleration. 3. At time t seconds (where t =0}, the particle P is moving in a plane with acceleration Y . (Br' - t)i + (8t 3))) When t = 2, the velocity of P is (16i + 3)) P T a) the velocity of P after t seconds b) the value of t when P is moving parallel to i. 4. Attime t = 0 a particle P is at rest at a point with position vector 4i 6j m with respect to a fixed origin O. The acceleration of P at time t seconds (where t=0) is (4t 3)i 6t jms Find: a) the velocity of P when t = ;l b) the position vector of P whent = 6 5. An object moves in a straight line from a point Q. At time t seconds the object has acceleration, a, where e a= - cos4nt ms , 0