STATISTICS Practice paper -1a.pdf, Exercises of Mathematics

Download STATISTICS Practice paper -1a.pdf and more Exercises Mathematics in PDF only on Docsity!

Practice paper – 1a

Practice paper —1a smetres & ° > 6 10 t seconds Figure 1 A toy car moves along a straight line. The line contains the fixed point O The toy car is modelled as a particle. Figure | shows the displacement-time graph for a model of the motion of the toy car, where s metres is the displacement of the toy car from O at time f seconds. Using the model, (a) find the speed of the toy car in the interval Oc 1 < 6 qd) (b) find the average speed of the toy car in the interval 0 <¢ < 10 @) (c) sketch the velocity-time graph for the motion of the toy car in the interval O< ¢ < 10 Q) (d) (i) Referring to your sketch, or otherwise, describe what happens to the motion of the toy car at the instant when f= 6 (ii) Explain why your answer to (i) represents a limitation of the model of the motion of the toy car at f= 6 (2) 1. The point 4 is 1.8m vertically above horizontal ground. At time f= 0, a small stone is projected vertically upwards with speed Ums' from the point 4. At time t= T seconds, the stone hits the ground. 1 The speed of the stone as it hits the ground is 10ms~ In an initial model of the motion of the stone as it moves from 4 to where it hits the ground + the stone is modelled as a particle moving freely under gravity + the acceleration due to gravity is modelled as having magnitude 10ms* Using the model, (a) find the value of U, (b) find the value of 7. 2. [In this question i and j are horizontal unit vectors.] A particle P of mass 5kg is moving on a smooth horizontal plane. The particle P is moving under the action of two forces (i+ 2j)N and (-ci— 10j)N, where c is a positive constant. The magnitude of the acceleration of P is 2ms” Find the value of ¢ G) 2) Question Scheme Marks AOs la) Speed = : oe(ms') BI 1.lb qd) 1(b) Average speed = wes MI | 3.la 2.4(ms') Al 1.1b Q) 1(c) v 1.1b 2 BI 10 Shape 8 3 Blft | 1.1b figs Q) 1(d)() The velocity (or speed or direction of motion) (of car) changes Bl 2.4 1(d)(ii) In reality this cannot occur instantaneously Bl 3.5b Q) Question Scheme Marks AOs 1(a) Complete method to produce an equation in U only M1 3.4 e.g. 10° =U? +2x gx18 oe Al | Lb OR a complete method where they find 7 first and use it to find an equation in U only Mi A correct equation in U only. Al U=8 (only this answer) Al 1.1b (3) (b) Complete method to find an equation in T only: M1 3.4 10=-8+gT or 18=107-— gf" or 1s- Sy 1 or 1.8= “8+ ost OR acomplete method if they split the time. T= 1.80e eg. 9/5 Al 1.1b Question Scheme Marks AOs 2. (1-c)i+(2-10)j MI 1.1b (I-c)i+(2-10)j =5a MI 3.la Use of magnitude of resultant = 10 or magnitude of a = 2 DMI | 2.1 (1-c)? +(2-10) =10° oe Al L.1b c=7 Al 1.1b 6) (5 marks) Notes: Allow use of column vectors 2. | MI Clear attempt to add the forces, seen or implied. Must collect i’s and j’s MI Use of F= Sa DMI | Must have a quadratic in ¢ only, dependent on first M1 Al Correct unsimplified quadratic in c Al | AOif they do not clearly reject e= —5 Question Scheme Marks AOs A(a) Equation of motion for 4 MI 3.3 1 T->mg=2ma Al 1.1b Q) 4(b) Equation of motion for B OR whole system equation MI 34 1 3mg —T =3ma OR 3mg — mg = Sma Al 1.1b Solve equations for a DMI 1.1b a= ! g Al 1.1b 3 : 1 2 1 V 2xZ exh or V = 2x5 exh MI 3.la V=jJgh Al 1.1b (6)