Mechnics (9709) M1 Topic 1 : s-t and v-t graph(9) Name: Score: Time: 1 (s03q3) The diagram shows the velocity-time graphs for the motion of two cyclists P and Q, whotravel in the same direction along a straight path. Both cyclists start from rest at the same point O and both accelerate at 2 m s 2 up to a speed of 10 m s 1. Both then continue at a constant speed of 10 m s 1. Q starts his journey T seconds after P. (i) Show in a sketch of the diagram the region whose area represents the displacement of P,fromO, at the instant when Q starts. [1] Given that P has travelled 16 m at the instant when Q starts, find (ii) the value of T, [3] (iii) the distance between P and Q when Q s speed reaches 10 m s 1. [2] (Q1) 徐汇宜山路校区 : 中山西路 1800 号兆丰环球大厦 13 楼 G 座 ( 九号线宜山路站 3 号口 ) 瑞玛教育考试研究院第 1/8 页
3 (s05q6) The diagram shows the velocity-time graph for a lift moving between floors in a building. The graph consists of straight line segments. In the first stage the lift travels downwards from the ground floor for 5 s, coming to rest at the basement after travelling 10 m. (i) Find the greatest speed reached during this stage. [2] The second stage consists of a 10 s wait at the basement. In the third stage, the lift travels upwards until it comes to rest at a floor 34.5 m above the basement, arriving 24.5 s after the start of the first stage. The lift accelerates at 2 m s 2 for the first 3 s of the third stage, reaching a speed of V ms 1. Find (ii) the value of V, [2] (iii) the time during the third stage for which the lift is moving at constant speed, [3] (iv) the deceleration of the lift in the final part of the third stage. [2] dx 徐汇宜山路校区 : 中山西路 1800 号兆丰环球大厦 13 楼 G 座 ( 九号线宜山路站 3 号口 ) 瑞玛教育考试研究院第 2/8 页
4 (w05q5) The diagram shows the displacement-time graph for a car s journey. The graph consists of two curved parts AB and CD, and a straight line BC. The line BC is a tangent to the curve AB at B and a tangent to the curve CD at C. The gradient of the curves at t = 0andt = 600 is zero, and the acceleration of the car is constant for 0 < t < 80 and for 560 < t < 600. The displacement of the car is 400 m when t = 80. (i) Sketch the velocity-time graph for the journey. [3] (ii) Find the velocity at t = 80. [2] (iii) Find the total distance for the journey. [2] (iv) Find the acceleration of the car for 0 < t < 80. [2] 徐汇宜山路校区 : 中山西路 1800 号兆丰环球大厦 13 楼 G 座 ( 九号线宜山路站 3 号口 ) 瑞玛教育考试研究院第 3/8 页
5 (s06q4) The diagram shows the velocity-time graph for the motion of a small stone which falls vertically from rest at a point A above the surface of liquid in a container. The downward velocity of the stone t s after leaving A is v ms 1. The stone hits the surface of the liquid with velocity 7 m s 1 when t = 0.7. It reaches the bottom of the container with velocity 5 m s 1 when t = 1.2. (i) Find (a) (b) the height of A above the surface of the liquid, the depth of liquid in the container. [3] (ii) Find the deceleration of the stone while it is moving in the liquid. [2] (iii) Given that the resistance to motion of the stone while it is moving in the liquid has magnitude 0.7 N, find the mass of the stone. [3] 徐汇宜山路校区 : 中山西路 1800 号兆丰环球大厦 13 楼 G 座 ( 九号线宜山路站 3 号口 ) 瑞玛教育考试研究院第 4/8 页
6 (w08q6) A train travels from A to B, a distance of 20 000 m, taking 1000 s. The journey has three stages. In the first stage the train starts from rest at A and accelerates uniformly until its speed is V ms 1.Inthe second stage the train travels at constant speed V ms 1 for 600 s. During the third stage of the journey the train decelerates uniformly, coming to rest at B. (i) Sketch the velocity-time graph for the train s journey. [2] (ii) Find the value of V. [3] (iii) Given that the acceleration of the train during the first stage of the journey is 0.15 m s 2,findthe distance travelled by the train during the third stage of the journey. [4] 7 (s10_41q2) The diagram shows the velocity-time graph for the motion of a machine s cutting tool. The graph consists of five straight line segments. The tool moves forward for 8 s while cutting and then takes 3 s to return to its starting position. Find (i) the acceleration of the tool during the first 2 s of the motion, [1] (ii) the distance the tool moves forward while cutting, [2] (iii) the greatest speed of the tool during the return to its starting position. [2] 1 v (m s ) 0.18 O 2 6 8 11 t (s) 徐汇宜山路校区 : 中山西路 1800 号兆丰环球大厦 13 楼 G 座 ( 九号线宜山路站 3 号口 ) 瑞玛教育考试研究院第 5/8 页
8 (w10_41q1) Two particles P and Q move vertically under gravity. The graphs show the upward velocity v m s 1 of the particles at time t s, for 0 t 4. P starts with velocity V m s 1 and Q starts from rest. (i) Find the value of V. [2] Given that Q reaches the horizontal ground when t = 4, find (ii) the speed with which Q reaches the ground, 1 v (m s ) [1] (iii) the height of Q above the ground when t = 0. V [2] P O 2 4 t (s) Q 徐汇宜山路校区 : 中山西路 1800 号兆丰环球大厦 13 楼 G 座 ( 九号线宜山路站 3 号口 ) 瑞玛教育考试研究院第 6/8 页
9 (w10_42q6) v (m s 1) V O 2.5 4.5 14.5 t (s) The diagram shows the velocity-time graph for a particle P which travels on a straight line AB, where v m s 1 is the velocity of P at time t s. The graph consists of five straight line segments. The particle starts from rest when t = 0 at a point X on the line between A and B and moves towards A. The particle comes to rest at A when t = 2.5. (i) Given that the distance XA is 4 m, find the greatest speed reached by P during this stage of the motion. [2] In the second stage, P starts from rest at A when t = 2.5 and moves towards B. The distance AB is 48 m. The particle takes 12 s to travel from A to B and comes to rest at B. For the first 2 s of this stage P accelerates at 3 m s 2, reaching a velocity of V m s 1. Find (ii) the value of V, [2] (iii) the value of t at which P starts to decelerate during this stage, [3] (iv) the deceleration of P immediately before it reaches B. [2] 徐汇宜山路校区 : 中山西路 1800 号兆丰环球大厦 13 楼 G 座 ( 九号线宜山路站 3 号口 ) 瑞玛教育考试研究院第 7/8 页
2 (s04q3) A boy runs from a point A to a point C. HepausesatC andthenwalksbacktowardsa until reaching the point B, where he stops. The diagram shows the graph of v against t, wherev ms 1 is the boy s velocity at time t seconds after leaving A. The boy runs and walks in the same straight line throughout. (i) Find the distances AC and AB. [3] (ii) Sketch the graph of x against t, where x metres is the boy s displacement from A. Show clearly the values of t and x when the boy arrives at C, when he leaves C, and when he arrives at B. [3] 徐汇宜山路校区 : 中山西路 1800 号兆丰环球大厦 13 楼 G 座 ( 九号线宜山路站 3 号口 ) 瑞玛教育考试研究院第 8/8 页