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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 Total
Marks 10 11 10 31
Score

Get Mathematics 9709 Topical Questions (2010-2021) for $14.5 per Subject. Attempt all the 3 questions Question 1 Code: 9709/41/O/N/11/7, Topic: - A particle$P$starts from a point$O$and moves along a straight line.$P$'s velocity$t$s after leaving$O$is$v \mathrm{~m} \mathrm{~s}^{-1}$, where $$v=0.16 t^{\frac{3}{2}}-0.016 t^{2}$$$P$comes to rest instantaneously at the point$A$.$\text{(i)}$Verify that the value of$t$when$P$is at$A$is 100.$[1]\text{(ii)}$Find the maximum speed of$P$in the interval$0< t <100$.$[4]\text{(iii)}$Find the distance$O A$.$[3]\text{(iv)}$Find the value of$t$when$P$passes through$O$on returning from$A$.$[2]$Question 2 Code: 9709/42/O/N/11/7, Topic: - A tractor travels in a straight line from a point$A$to a point$B$. The velocity of the tractor is$v \mathrm{~m} \mathrm{~s}^{-1}$at time$t \mathrm{~s}$after leaving$A$.$\text{(i)}$The diagram shows an approximate velocity-time graph for the motion of the tractor. The graph consists of two straight line segments. Use the graph to find an approximation for$\text{(a)}$the distance$A B$,$[2]\text{(b)}$the acceleration of the tractor for$0< t <400$and for$400< t <800$.$[2]\text{(ii)}$The actual velocity of the tractor is given by$v=0.04 t-0.00005 t^{2}$for$0 \leqslant t \leqslant 800$.$\text{(a)}$Find the values of$t$for which the actual acceleration of the tractor is given correctly by the approximate velocity-time graph in part$\text{(i)}$.$[3]$For the interval$0 \leqslant t \leqslant 400$, the approximate velocity of the tractor in part$\text{(i)}$is denoted by$v_{1} \mathrm{~m} \mathrm{~s}^{-1}\text{(b)}$Express$v_{1}$in terms of$t$and hence show that$v_{1}-v=0.00005(t-200)^{2}-1$.$[2]\text{(c)}$Deduce that$-1 \leqslant v_{1}-v \leqslant 1$.$[2]$Question 3 Code: 9709/43/O/N/11/7, Topic: - A car of mass$600 \mathrm{~kg}$travels along a straight horizontal road starting from a point$A$. The resistance to motion of the car is$750 \mathrm{~N}$.$\text{(i)}$The car travels from$A$to$B$at constant speed in$100 \mathrm{~s}$. The power supplied by the car's engine is constant and equal to$30 \mathrm{~kW}$. Find the distance$A B$.$[3]\text{(ii)}$The car's engine is switched off at$B$and the car's speed decreases until the car reaches$C$with a speed of$20 \mathrm{~m} \mathrm{~s}^{-1}$. Find the distance$B C$.$[3]\text{(iii)}$The car's engine is switched on at$C$and the power it supplies is constant and equal to$30 \mathrm{~kW}$. The car takes$14 \mathrm{~s}$to travel from$C$to$D$and reaches$D$with a speed of$30 \mathrm{~m} \mathrm{~s}^{-1}$. Find the distance$C D.[4]\$

Worked solutions: P1, P3 & P6 (S1)

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