CAIE M1 (Mechanics 1) 2020 Specimen

1 A rticle \(P\) is p j ected rticallyw ard with \(\mathbf { p }\) ed \(\mathrm { ms } ^ { - 1 }\) frm a \(\dot { \mathrm { p } } \mathrm { n } \mathbf { d }\) b gd

1. Fid b g eatest b in a th gd each dy \(P\).
2. Fid \(\mathbf { b }\) to al time frm \(\mathrm { p } \dot { \mathrm { p } }\) ectim il \(P\) retu \(\mathbf { B }\) to \(\mathbf { b } \mathbf { g d }\)

2 ACB tan resistan e of mag itd ( ) N acts \(\boldsymbol { \infty }\) car \(\boldsymbol { 0 }\) mass \(\boldsymbol { 0 }\) g

1. Th car is mi gr lor straig le lro de taco tan sp e \(\varnothing \quad 3 \mathrm {~ms} ^ { - 1 }\). Fid \(n \mathrm {~W} , \mathrm { t } \mathbf { b }\) rate at wh cht b eg \(\mathbf { B }\) the car is work g
2. Th car tra ls at a co tan sp ed n a h ll in lie d at an ag e \(\boldsymbol { 6 } \theta ^ { \circ }\) to to b izo al, wh re \(\sin \theta ^ { \circ } = \frac { 1 } { 20 }\), w ittl b eg e wo kg t\\( \)\mathbb { N }$. Fid b sp e \(\boldsymbol { \varnothing }\) th car.

3 Th ee small smo h se res \(A , B\) ad \(C 6\) eq l radi ad 6 masses \(4 \mathrm {~g} \quad 2 \mathrm {~g}\) ad 3 g resp ctie ly, lie in th todr in a strait lie o a smo hb izt al p ae. In tially, \(B\) ad \(C\) are at rest ad \(A\) is mi g ard \(B\) with sp ed \(6 \mathrm {~ms} ^ { - 1 }\). After th cb liso with \(B\), se re \(A\) co in s to mo in the same d rectim withs p ed \(\mathrm { ms } ^ { - 1 }\).

1. Fid b sp e \(\boldsymbol { \Phi } \quad B\) after th s cb liso Se re \(B\) cb lid s with \(C\).I it \(h\) s cb lisd \(\mathbf { b }\) se two se res co lesce tof \(\mathbf { o }\) m am \(\mathbf { b }\) ect \(D\).
2. Fid b sp e \(D\) after th s cb lisin
   \includegraphics[max width=\textwidth, alt={}, center]{0a1cec7f-f9d1-4628-b979-443514c73eb9-05_65_1652_1146_242}

4 A \(\boldsymbol { p }\) rticle of mass \(\emptyset \mathrm { g }\) is \(\mathbf { n }\) a rg p an in lin d at an an \(\mathrm { e } \boldsymbol { 6 } \mathbf { B } ^ { \circ }\) to th \(\mathbf { b }\) izn tal. A fo ce \(\boldsymbol { 6 }\) mag te \(\quad\) z N, actig at an ag e 6 O \(^ { \circ }\) ab a lin 6 g eatest sle 6 th p aB , is s ed to p e n th \(\mathbf { P }\) rticle frm slid g n th p as. Th co fficient

5 A car 6 mass \(\mathbb { I } \quad\) g is p lig a trailer 6 mass \(\theta \quad\) g ah ll in lin d at an ag e \(6 \sin ^ { - 1 } ( \mathbb { I } )\) ) to th b izo al. Th car and to trailer are co cted b a lig rig d -b r wh ch is \(\boldsymbol { \rho }\) rallel to th ro d Th d iv g fo ce \(\varnothing\) th car's eg A is \(\theta \mathrm { N }\) ad th resistan es to th car ad trailer are \(\theta \mathrm { N }\) ad (1) N resp ctie ly.

1. Fid b acceleratio th sy tem ad b tensio it b tw -b r.
2. Wh it b car ad railer are tra llig tasp e \(\boldsymbol { \Theta } \quad \mathbf { b } \mathrm { ms } ^ { - 1 } , \mathrm { t } \mathbf { b }\) divg \(\mathbf { o }\) ce b cm es zero Fid th time, in sect , \(\mathbf { b }\) fo e the sy tem cm es to rest ad th fo ce in th ro \(\mathbf { r d }\) ig th s time.

6 A \(\boldsymbol { p }\) rticle \(P \mathrm {~m}\) s ira straitg lie . Tb ± lo ity \(v \mathrm {~ms} ^ { - 1 }\) at time \(t \mathrm {~s}\) is g ஓ ity $$\begin{array} { l l } v = 5 t ( t - 2 & \text { fo } 0 \leqslant t \leqslant 4
v = k & \text { fo } 4 \leqslant t \leqslant 4
v = 82 \quad t & \text { fo } 4 \leqslant t \leqslant \Omega \end{array}$$ wh re \(k\) is a co tan.

1. Fid \(k\).
2. Sk tcht b lo ity ime g aff \(\mathbf { 0 } \quad 0 \leqslant t \leqslant 0\)
3. Fid bet \(\mathbf { 6 }\) le \(\mathrm { s } \mathbf { 6 } t\) fo wh cht b acceleratio \(P\) is \(\mathbf { p }\) itie .
4. Fid \(\mathbf { b }\) to ald stan e trac lledy \(P\) irt \(\mathbf { b }\) in era \(10 \leqslant t \leqslant 0\)

7
\includegraphics[max width=\textwidth, alt={}, center]{0a1cec7f-f9d1-4628-b979-443514c73eb9-12_248_674_260_699} Two \(\boldsymbol { \rho }\) rticles \(A\) ad \(B , 6\) masses 08 k ad 0 g resp ctie ly, are co cted \(\varphi\) a lig inex en ib e strig Particle \(A\) is p aced \(\mathbf { n }\) ab izb al sn face. Th strig \(\boldsymbol { p }\) sses rasmall smo hp ley \(P\) fiæ d at th ed 6 th su face, and \(B \mathbf { h }\) g freely. Th \(\mathbf { b }\) izo alsectin 6 th strig \(A P\), is \(\mathbf { 6 }\) leg \(\mathrm { h } \otimes \mathrm { m }\) (see id ag am). Th \(\boldsymbol { p }\) rticles are released rm rest witb lo ectim of th strig atı.

1. Gie it \(\mathbf { h }\) th sn face is smo lf id \(\mathbf { b }\) time tak if \(\mathbf { D }\) A tor eacht \(\mathbf { b }\) p ley. [
2. It is \(\dot { \mathbf { g } }\) ven in tead that th sn face is rg ad th t th sp ed \(6 A\) immed ately \(\mathbf { b }\) fo e it reach s th p leỳ \(\mathrm { s } v \mathrm {~ms} ^ { - 1 }\). Th wo ld ag in t frictim \(\mathrm { s } A \mathrm {~m}\) s frm rest to b p leyi s 2 J . Use an ee rgn eth \(\quad\) f id \(v\). [4] If B e th follw ig lin dpg to cm p ete th an wer(s) to ay q stin (s), th q stin \(\mathrm { m } \quad \mathbf { b } \quad \mathrm { r } ( \mathrm { s } )\) ms tb clearlys n n