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### HENRYTAIGO

#### Cambridge International AS and A Level

 Name of student HENRYTAIGO Date Adm. number Year/grade HenryTaigo Stream HenryTaigo Subject Mechanics 1 (M1) Variant(s) P41, P42, P43 Start time Duration Stop time

Qtn No. 1 2 3 4 5 6 Total
Marks 8 7 8 7 9 8 47
Score

Get Mathematics 9709 Topical Questions (2010-2021) for $14.5 per Subject. Attempt all the 6 questions Question 1 Code: 9709/41/M/J/13/5, Topic: - A light inextensible string has a particle$A$of mass$0.26 \mathrm{~kg}$attached to one end and a particle$B$of mass$0.54 \mathrm{~kg}$attached to the other end. The particle$A$is held at rest on a rough plane inclined at angle$\alpha$to the horizontal, where$\sin \alpha=\frac{5}{13}$. The string is taut and parallel to a line of greatest slope of the plane. The string passes over a small smooth pulley at the top of the plane. Particle$B$hangs at rest vertically below the pulley (see diagram). The coefficient of friction between$A$and the plane is$0.2$. Particle$A$is released and the particles start to move.$\text{(i)}$Find the magnitude of the acceleration of the particles and the tension in the string.$[6]$Particle$A$reaches the pulley$0.4 \mathrm{~s}$after starting to move.$\text{(ii)}$Find the distance moved by each of the particles.$[2]$Question 2 Code: 9709/42/M/J/13/5, Topic: - A car of mass$1000 \mathrm{~kg}$is travelling on a straight horizontal road. The power of its engine is constant and equal to$P \mathrm{~kW}$. The resistance to motion of the car is$600 \mathrm{~N}$. At an instant when the car's speed is$25 \mathrm{~m} \mathrm{~s}^{-1}$, its acceleration is$0.2 \mathrm{~m} \mathrm{~s}^{-2}$. Find$\text{(i)}$the value of$P$,$[4]\text{(ii)}$the steady speed at which the car can travel.$[3]$Question 3 Code: 9709/43/M/J/13/5, Topic: - A particle$P$is projected vertically upwards from a point on the ground with speed$17 \mathrm{~m} \mathrm{~s}^{-1}$. Another particle$Q$is projected vertically upwards from the same point with speed$7 \mathrm{~ms}^{-1}$. Particle$Q$is projected$T$seconds later than particle$P$.$\text{(i)}$Given that the particles reach the ground at the same instant, find the value of$T$.$[2]\text{(ii)}$At a certain instant when both$P$and$Q$are in motion,$P$is$5 \mathrm{~m}$higher than$Q.$Find the magnitude and direction of the velocity of each of the particles at this instant.$[6]$Question 4 Code: 9709/41/O/N/13/5, Topic: - A lorry of mass$15000 \mathrm{~kg}$climbs from the bottom to the top of a straight hill, of length$1440 \mathrm{~m}$, at a constant speed of$15 \mathrm{~m} \mathrm{~s}^{-1}$. The top of the hill is$16 \mathrm{~m}$above the level of the bottom of the hill. The resistance to motion is constant and equal to$1800 \mathrm{~N}$.$\text{(i)}$Find the work done by the driving force.$[4]$On reaching the top of the hill the lorry continues on a straight horizontal road and passes through a point$P$with speed$24 \mathrm{~m} \mathrm{~s}^{-1}$. The resistance to motion is constant and is now equal to$1600 \mathrm{~N}$. The work done by the lorry's engine from the top of the hill to the point$P$is$5030 \mathrm{~kJ}$.$\text{(ii)}$Find the distance from the top of the hill to the point$P$.$[3]$Question 5 Code: 9709/42/O/N/13/5, Topic: - A particle$P$moves in a straight line.$P$starts from rest at$O$and travels to$A$where it comes to rest, taking 50 seconds. The speed of$P$at time$t$seconds after leaving$O$is$v \mathrm{~m} \mathrm{~s}^{-1}$, where$vis defined as follows. \begin{aligned} \text { For } 0 \leqslant t \leqslant 5, & v=t-0.1 t^{2}, \\ \text { for } 5 \leqslant t \leqslant 45, & v \text { is constant, } \\ \text { for } 45 \leqslant t \leqslant 50, & v=9 t-0.1 t^{2}-200. \end{aligned}\text{(i)}$Find the distance travelled by$P$in the first 5 seconds.$[3]\text{(ii)}$Find the total distance from$O$to$A$, and deduce the average speed of$P$for the whole journey from$O$to$A$.$[6]$Question 6 Code: 9709/43/O/N/13/5, Topic: - A car travels in a straight line from$A$to$B$, a distance of$12 \mathrm{~km}$, taking 552 seconds. The car starts from rest at$A$and accelerates for$T_{1} \mathrm{~s}$at$0.3 \mathrm{~m} \mathrm{~s}^{-2}$, reaching a speed of$V \mathrm{~m} \mathrm{~s}^{-1}$. The car then continues to move at$V \mathrm{~m} \mathrm{~s}^{-1}$for$T_{2} \mathrm{~s}$. It then decelerates for$T_{3} \mathrm{~s}$at$1 \mathrm{~ms}^{-2}$, coming to rest at$B$.$\text{(i)}$Sketch the velocity-time graph for the motion and express$T_{1}$and$T_{3}$in terms of$V$.$[3]\text{(ii)}$Express the total distance travelled in terms of$V$and show that$13 V^{2}-3312 V+72000=0$. Hence find the value of$V$.$[5]\$

Worked solutions: P1, P3 & P6 (S1)

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