Advanced level 2025 Littoral Regional Mock mathematics mechanics 3
Advanced level 2025 Littoral Regional Mock mathematics mechanics 3
b) A car of mass 900 kg can attain a maximum speed of 50ms‘1 when traveling along a level road against a constant
resistance to motion of 350N.
( i ) Find the rate at which the engine of the car is working. (3 marks)
i
The car now begins to ascend a hill inclined at an angle of sin — to the horizontal . Given that the engine works
60
at the same rate and the resistance to motion is unchanged,
(ii) Find the maximum speed of the car up the hill. (3 marks)
7.
(a) A particle starts moving from rest in a circular path, and uniformly accelerated to an angular speed of 60 revolutions
per minute. The particle maintains this speed for 5 minutes and them retards to rest in the next one minute. The total
time taken for the motion is 15 minutes.
Determine the number of revolutions made by the particle.
( ii ) Find the angle turned by the particle before coming to rest.
A particle P of mass m is attached to one end I i of a light elastic string A H of natural length a and modulus of
elasticity y 3 //ig. The other end A is attached to a fixed ceiling. The particle /‘ moves with constant angular speed m
in a horizontal circle with centre O y where ( ) is vertically below /\ , with the string A H making an angle of 30‘ with
the vertical. Show that:
|,u–|=—
, 2>/ 3 g
Of –= 1
(b)
( i ) (4 marks)
(ii ) (3 marks)
5<;
8.
Two independent events A and H are such that P ( A ) =0.4 and H i A n H ) = 0.13. Find:
During a movie night in a cinema hall, 65% of the spectators are women, 25% are men and the rest are children. 15%
of the women, 5% of the men and 2% of the children are eligible for a free ticket during the next movie night. A
person is selected at random from the cinema hall. Find, to 3 decimal places, the probability that the person is:
(b)
