9709/Oct Nov/2002/4/Q7

A particle P starts to move from a point O and travels in a straight line. At time ts after P starts to

move its velocity is v ms^-1, where v - 0.12t - 0.0006t².

(i) Verify that P comes to instantaneous rest when t = 200, and find the acceleration with which it

starts to return towards O.

(ii) Find the maximum speed of P for 0 <= t <= 200.

(iii) Find the displacement of P from O when t = 200.

(iv) Find the value of t when P reaches O again.

Solution:

 

Reference: PYQ - Oct/Nov 2002 Paper 4 Q7

9709/Oct Nov/2002/4/Q4

Two particles A and B are projected vertically upwards from horizontal ground at the same instant.

The speeds of projection of A and B are 5ms^-1 and 8ms^-1 respectively. Find

(i) the difference in the heights of A and B when A is at its maximum height,

(ii) the height of A above the ground when B is 0.9m above A.

Solution:

Reference: PYQ - Oct/Nov 2002 Paper 4 Q4

9709/Oct Nov/2002/4/Q3

A light inextensible string has its ends attached to two fixed points A and B, with A vertically above B. A smooth ring R, of mass 0.8 kg, is threaded on the string and is pulled by a horizontal force of magnitude X newtons. The sections AR and BR of the string make angles of 50^o and 20^o  respectively with the horizontal, as shown in the diagram. The ring rests in equilibrium with the string taut. Find

(i) the tension in the string,

(ii) the value of X.

Solution:

Reference: PYQ - Oct/Nov 2002 Paper 4 Q3

9709/Oct Nov/2002/3/Q6

Let f(x) = (6+7x) / [(2-x)(1+x^2)]
(i) Express f(x) in partial fractions.
(ii) Show that, when x is sufficiently small for x^4 and higher powers to be neglected, f(x) = 3 + 5x - 1/2 x^2 - 15/4x^3

Solution:
i)

ii)

Reference: PYQ - Oct/Nov 2002 Paper 3 Q6