1)A bus 18.8m long moving at 50km/h overtakes a second bus moving at 45 km/h in 22 and a 1/2 seconds.Find the length of the second bus.
2)Kiriari is a market centre 600 km from Kisumu town.A bus starts from Kisumu for Kiriari at 7 am at an average speed of 80km/h.At 8:30 am a car started from Kisumu to Kiriari and moved at an average speed of 120km/h;
a)Find the distance the bus covered before the car started moving.
b)Find the relative speed for the two vehicles
c)Find the time the car overtook the bus.
d) Find the distance covered by the car before overtaking the bus.
3)The figure below shows a velocity time graph of an object which accelerates from rest to a velocity Vm/s then decelerates to rest In a total time of 54 sec.If the whole journey is 810 km;
a)Find the value of V
b)Find the deceleration given the initial acceleration is 1 and 2/3 m/s^2.
4)A car accelerated from rest to a velocity of 10m/s.It travelled at this velocity for 20sec and then came to a stop 5 sec.Find;
a)The initial acceleration
b)The distance traveled
5)If the total distance travelled in the 80 sec is 920m.calculate;
a)The value of V
b)The acceleration during the first 15 sec
c)The distance traveled in the final 40 seconds.
6)In the figure below P and Q are points on OA and OB respectively such that OP:PA=3:2 and OQ:QB=1:2 AQ and PQ intersect at T.Given that OA= a and OB=b;
a)Express AQ and PQ in terms of a and b.
b)Taking BT=kBP and AT=hAQ where h and k are real numbers.
i)Find two expressionns for OT in terms of a and b.
ii)Use the expression above in b(i) above to find the values of h and k.
c)Show that B,T and P are collinear.
7)Given that vectors a=3i-j+2k,b=4i+2j-k and p=2a-b.
a)Express p in the terms of i,j and k.
b)Hence calculate/p/ correct to 3 significant figures
8)The point A,B and C lies on a straight line.The position vectors of A and C are 2i+3j+9k and 5i-3j+4k respectively;B divides AC internally in the ratio 2:1.Find;
a) Position vector of B.
9)Given that the position vectors of point P is p=5a-2b where a=(3/2) and b=(4/1).
a)Column vector of p.
b)P' the image of P under translation vector(-4/-6)
10)A translation map point A(6,4) onto A'(10,8).
a)Determine the translation vector.
b)A point B' is the is the image of B(4,10) under the same translation.Find the length A'B' leaving your answer in surd form.
11)P and Q are two points such that OP=4i+5j-3k.M is a point that divides PQ externally in the ratio 3:2.Find the coordinates of M.
12)The position vectors of points x,y and z are x=ti+2j;y=2i+3j;z=3i+4j and respectively.If the points x,y and z are collinear,Find the value of t.
13)A sector of a circle of radius 42cm subtended an angle of 120° at the centre of the circles.The sector is folded into an inverted right cone.Calculate:-
a)The base radius of the cone.
b)To one decimal place the vertical height of the cone.
14)The histogram below represents the distribution of marks obtained Ina test.The frequency of the second class is 3.