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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 6 7 7 7 6 6 39
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/12/3, Topic: - A load of mass$160 \mathrm{~kg}$is pulled vertically upwards, from rest at a fixed point$O$on the ground, using a winding drum. The load passes through a point$A, 20 \mathrm{~m}$above$O$, with a speed of$1.25 \mathrm{~m} \mathrm{~s}^{-1}$(see diagram). Find, for the motion from$O$to$A$,$\text{(i)}$the gain in the potential energy of the load,$\text{(ii)}$the gain in the kinetic energy of the load.$$The power output of the winding drum is constant while the load is in motion.$\text{(iii)}$Given that the work done against the resistance to motion from$O$to$A$is$20 \mathrm{~kJ}$and that the time taken for the load to travel from$O$to$A$is$41.7 \mathrm{~s}$, find the power output of the winding drum.$$Question 2 Code: 9709/42/M/J/12/3, Topic: - A particle$P$moves in a straight line, starting from the point$O$with velocity$2 \mathrm{~m} \mathrm{~s}^{-1}$. The acceleration of$P$at time$t \mathrm{~s}$after leaving$O$is$2 t^{\frac{2}{3}} \mathrm{~m} \mathrm{~s}^{-2}$.$\text{(i)}$Show that$t^{\frac{5}{3}}=\frac{5}{6}$when the velocity of$P$is$3 \mathrm{~m} \mathrm{~s}^{-1}$.$\text{(ii)}$Find the distance of$P$from$O$when the velocity of$P$is$3 \mathrm{~ms}^{-1}$.$$Question 3 Code: 9709/43/M/J/12/3, Topic: - A particle$P$travels from a point$O$along a straight line and comes to instantaneous rest at a point$A$. The velocity of$P$at time$t \mathrm{~s}$after leaving$O$is$v \mathrm{~m} \mathrm{~s}^{-1}$, where$v=0.027\left(10 t^{2}-t^{3}\right)$. Find$\text{(i)}$the distance$O A$,$\text{(ii)}$the maximum velocity of$P$while moving from$O$to$A$.$$Question 4 Code: 9709/41/O/N/12/3, Topic: - A particle$P$of mass$0.5 \mathrm{~kg}$rests on a rough plane inclined at angle$\alpha$to the horizontal, where$\sin \alpha=0.28$. A force of magnitude$0.6 \mathrm{~N}$, acting upwards on$P$at angle$\alpha$from a line of greatest slope of the plane, is just sufficient to prevent$P$sliding down the plane (see diagram). Find$\text{(i)}$the normal component of the contact force on$P$,$\text{(ii)}$the frictional component of the contact force on$P$,$\text{(iii)}$the coefficient of friction between$P$and the plane.$$Question 5 Code: 9709/42/O/N/12/3, Topic: - A car travels along a straight road with constant acceleration$a \mathrm{~m} \mathrm{~s}^{-2}$. It passes through points$A, B$and$C$; the time taken from$A$to$B$and from$B$to$C$is$5 \mathrm{~s}$in each case. The speed of the car at$A$is$u \mathrm{~m} \mathrm{~s}^{-1}$and the distances$A B$and$B C$are$55 \mathrm{~m}$and$65 \mathrm{~m}$respectively. Find the values of$a$and$u$.$$Question 6 Code: 9709/43/O/N/12/3, Topic: - A particle$P$is projected vertically upwards, from a point$O$, with a velocity of$8 \mathrm{~m} \mathrm{~s}^{-1}$. The point$A$is the highest point reached by$P$. Find$\text{(i)}$the speed of$P$when it is at the mid-point of$O A$,$\text{(ii)}$the time taken for$P$to reach the mid-point of$O A$while moving upwards.$\$

Worked solutions: P1, P3 & P6 (S1)

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