Linear motion Questions
1. A passenger train travelling at 25km/h is moving in the same direction as a truck travelling at 30km/h. The railway line runs parallel to the road and the truck takes 1 ½ minutes to over take the train completely.
- Given that the truck is 5 metres long determine the length of the train in metres. (6 marks)
- The truck and the train continue moving parallel to each other at their original speeds. Calculate the distance between them 4 minutes and 48 seconds after the truck overtakes this train. (4 marks)
2. Two passenger trains A and B, 240m apart are travelling at 164km/h and 88km/h respectively approach one another on a straight railway line. Train A is 150 metres long. Determine the time in seconds that elapses before the two trains completely pass each other. (3mks)
3. A minibus covered a distance of 210km at an average speed of 90km/h. If it travelled ⅔ of the distance at a speed of 105 km/h, at what speed did it travel the rest of the distance? (3mks)
4. Two buses P and Q leave Kisumu at 7.30 am and 9.30 am respectively. If their speeds are 60km/h and 100km/h respectively, find when Q catches up with P. (3mks)
5. (a) A boat’s speed in still water is 4km/h. It cruises in a section AB of a river whose speed downstream is x km/h. If the boat takes 2 hrs more in return journey and AB = 6km. find the value of x and the total duration of the journey (8mks)
(b) The whole journey in (a) above ended at 3.34am. Find the departure time in 24 hour clock system (2mks)
6. The figure below is a velocity time graph for a car.
y
80
0 4 20 24 x
Time (seconds)
(a) Find the total distance traveled by the car. (2 marks)
(b) Calculate the deceleration of the car. (2 marks)
7. A bus started from rest and accelerated to a speed of 60km/h as it passed a billboard. A car moving in the same direction at a speed of 100km/h passed the billboard 45 minutes later. How far from the billboard did the car catch up with the bus? (3mks)
8. Nairobi and Eldoret are each 250km from Nakuru. At 8.15am a lorry leaves Nakuru for Nairobi. At 9.30am a car leaves Eldoret for Nairobi along the same route at 100km/h. both vehicles arrive at Nairobi at the same time.
(a) Calculate their time of arrival in Nairobi (2mks)
(b) Find the cars speed relative to that of the lorry. (4mks)
(c) How far apart are the vehicles at 12.45pm. (4mks)
9. A train whose length is 86 metres is traveling at 28 km/h in the same direction as a truck whose length is 10 metres. If the speed of the truck is 60 km/ h and is moving parallel to the train.
Calculate the time it takes the truck to overtake the train completely. (3mks)
10. The distance between towns A and B is 360km. a minibus left A at 8.15am and traveled towards B at an average speed of 90km/hr. A matatu left B two and a third hours later on the same day and traveled towards A at an average speed of 110km/hr.
a) i) At what time did the two vehicles meet?
ii) How far from A did the vehicles meet?
b) A motorist started from his home at 10.30am on the same day and travelled at an average speed of 100km/hr. he arrived at B at the same time as the minibus. Calculate the distance from A to his house. (10 mks)
11. A track traveling at 60 km/hr takes 1 hour 20 minutes more than a van traveling at 80 km/hr to cover the distance from Thika to Eldoret
Calculate:
a) The distance from Thika to Eldoret (2 marks)
b) If the track leaves Thika at 2230 hrs and the van leaves Thika 30 minutes later, find the time the van catches up with the track (3 marks)
c) At 2330 hrs a saloon car left Eldoret for Thika traveling at 120 km/hr and met the van at town K. find :
- The time they met (3 marks)
- The distance between town K and the track at the time in C(I) above (2 marks)
12. Two motorists Kinyua and Nyaboke travelled between two towns K and M which
are 580km apart. Kinyua started from K at 6.20 a.m and traveled towards M at 90km/hr.
Nyaboke started from town M 1 2/3 hours later and traveled towards town K at an average
speed of 120km/h. At a small shopping centre along the way, Kinyua had a snack and car
check for 20 minutes before proceeding
(a) (i) How far from town M did they meet?
(ii) At what time did they meet?
(b) A rally driver starts from town M going to town k at 9.30a.m. If he averages 180km/hr,
Calculate the distance from K and the time when the rally driver overtook Nyaboke
13. The distance between two towns A and B is 150km. A car starts from town A at
10.00a.m and travels at an average speed of 80km/h towards B. A transit lorry travels
from B at 10:15a.m towards town A at an average speed of 40km/h. At what time will
the two vehicles meet?
14. The diagram below shows the speed-time graph for a bus traveling between two towns.
The bus starts from rest and accelerates uniformly for 50seconds. It then travels at a constant
speed for 150seconds and finally decelerates uniformly for 100seconds.
Given that the distance between the two towns is 2700m, calculate the
(a) maximum speed in km/h, the bus attained
(b) acceleration
(c) distance the bus traveled during the last 50seconds
(d) time the bus takes to travel the first half of the journey
15. A cyclist covers a distance of 45 kilometres at a speed of 10km/h and a further 45
kilometres at 15km/h. Find his average speed for the journey
16. A lorry left town A for town B 1¼ hours before a car. The lorry and the car are traveling
in the same direction at 80kmh-1 and 120kmh-1 respectively. After the overtake, the car
moved for another hours before reaching town B. Calculate:
(a) The time the car took before overtaking the lorry completely
(b) The distance between the two towns
(c) The time the lorry will take to reach town B after the arrival of the car
17. A country bus left Nairobi at 10.45a.m and traveled towards Mombasa at an average speed
of 60km/h. A matatu left Nairobi at 1:15p.m on the same day and traveled along the same
road at an average speed of 100km/h. The distance between Nairobi and Mombasa is 500km.
(a) Determine the time of the day when the matatu overtook the bus
(b) Both vehicles continue towards Mombasa at their original speeds. How long had the
matatu waited before the bus arrived?
18. Two passenger trains A and B which are 240m apart are travelling at 164km/h and 88km/h
respectively approach on another one a straight railway line. Train A is 150m long and train
B is 100m long. Determine the time in seconds that elapses before the two trains completely
pass each other
19. A bus 5m long completely overtakes a trailer 15m long travelling in the same direction in 4.8.
seconds. If the speed of the bus is 40 km/hr, determine the speed of the trailer in km/hr.
20. Find the LCM and GCD of the following numbers: 2 x 3 x 53 and 24 x 32 x 52.
21. A boat sails from a point A to a point B upstream, a distance of 30 km and back to A in 3hrs 12
min. The current in the river is flowing at 5km/hr. Determine the speed of the boat in still water.
22.. Two friends Ojwang and David live 40 km apart. One day Ojwang left his house at 9.00 a.m.
and cycled towards David’s house at an average speed of 15 km/h. David left his house at 10.30
a.m. on the same day and cycled towards Ojwang’s house at an average speed of 25 km/h.
a) Determine
(i) The distance from Ojwang’s house, where the two friends met.
(ii) The time they met.
(iii) How far Ojwang was from David’s house when they met.
- The two friends took 10 minutes at the meeting point and they cycled to David’s
house at an average speed of 12 km/h. Find the time they arrived at David’s house.
23. Mr. Kamau left town S at 6.00a.m and travels at an average speed of 24km/hr towards R.
Mrs. Ronoh left town R to town S 10minutes later and arrived at 7.00a.m. If distance
RS = 42km , find;
(a) Where and when they will meet
(b) The time Kamau arrived at R
(c) If at 7.00a.m another traveler left S and travels towards R at speed twice that of
Mrs. Ronoh, find where and when Mr. Kamau was overtaken by the traveler if so
24. A train 100m long travelling at 72km/hr, overtakes another train traveling in the same
direction at 56km/hr and passes it completely in 54 seconds.
i) Find the length of the second train
ii) Find also the time they would have taken to pass one another if they had been traveling
at these speeds in opposite directions
25. An unskilled worker may either walk to work along a route 5km to take a bus journey of 7km.
The average speed of the bus is 24km/hr faster than his average speed. Taking the average
walking speed as x km/hr;
(a) Write down expressions for time of the journey;
(i) When walking
(ii) When using the bus
(b) The journey by bus takes 36 minutes less than the journey on foot, find his walking speed
(c) Hence find the time he takes to talk to work
26. At 1.50 p.m. a matatu is traveling at 80 km/h and it is 40 km behind a motorcycle traveling
at 60 km/h.
(a) After how long will the matatu overtake the motorcycle?
(b) At what time will the matatu overtake the motorcycle?
27. A bus left Nairobi at 8:00a.m and traveled towards Kisumu at an average speed of 80km/h.
At 8.30a.m, a car left Kisumu towards Nairobi at an average speed of 120km/hr. Given that
the distance between Nairobi and Kisumu is 400km, Calculate:-
(a) The time the car arrived in Nairobi
(b) The time the two vehicles met
(c) The distance from Nairobi to the meeting point
(d) The distance of the bus from Kisumu when the car arrived in Nairobi
28. Two trucks A and B travelling at 28km/hr and 26km/hr respectively approach one another on
a straight road. Truck A is 10m long, while truck B is 15m long. Determine the time in seconds
that elapses before the trucks completely pass each other
Linear motion Answers
1. Distance covered by Kinyua in 12/3hrs
= 5 x 90 = 150km
Distance traveled by Nyaboke during the rest = (1/3 x 120) = 40km
x = 390 – x 120x = 90(390 – x)
90 120
= 167.1km
Time = 167.1 = 1.86
90
8.33 + 1.86 = 10.19; they met at = 10.11a.m
580 – (150 + 167 .1) = 262.9km from M
Before the rally driver started, Nyaboke had traveled for 1 ½ hrs
( 3/2 x 120) = 180km
x = x + 180
120 80
180x – 120x = 21600
x = 360km
Distance from K = 580 – (180 + 360)
x = 40km
Time = 540 = 3hrs
180
(9.30 + 3hrs) = 12.30p.m
2. Distance covered by the car after 15 min =( ¼ x 80)km = 20km
Distance covered together = 130km
Relative speed = (80 + 40) = 120km/h
Time taken to meet
= (130) hrs
120
= 1hr 5 min
Time they met = 10:15 a.m +
1:05
11:20 a.m
3. . a) ½ X 50h + ½ X 100 h + 150h = 2700
225h = 2700
H = 2700 = 12m/s
225
Maximum speed = 12 x 60 x 60
1000
= 43.2km/h
b) Acceleration = 12/50 m/s
= 6/25 m/s
c) ½ X 50 x 6
150 m
d) Time for half of journey
½ X 12 (50 + t + t) = ½ X 2700
6(50 + 2t) = ½ X 2700
50 + 2t = 225
T = 225 – 50 = 87.5
2
Total time
= 50 + 87.5 = 137.5 sec
4. Time taken at 10km
= 45/10 = 4.5 hrs
Time taken at 15km/hr
45/15 = 3hrs
Total time taken = (4.5 + 3) = 7.5
(4.5 + 3) = 7.5 hrs
Average speed
= 90/7.5
= 12km/hr
5. D = 5 x 80 + 50
4 1000
= 100.05km
Speed = 120 – 80 = 40km/h
T = D = 100.05
S 40
= 2.50125hours
(b) D = S xT = 120 + 100.05 + 199
4000 800
= 120 x 11000
40000
= 330km
(c) Total time = 330
80
= 41/8hrs
Time lapse = 41– 5 + 100.05 + 199
8 4 40000 800
= 41 – 4
8 = 1/8hrs
6. a) Distance traveled by bus before the matatu started off the journey is
Distance = speed x time
= 60 x 2 ½
= 150km
Relative speed = 100- 60 = 40km/hr
The matatu would cover the bus head start of 150km in 150/40 hrs = 3.75hrs = 3hrs 45 min
The matatu will overtake the bus after 3hrs 45 minutes
This will be 1:15 + 3:45 = 5.00pm
b) Time taken by the matatu to complete the remaining 350km = 350/100 = 3 ½ hrs
= 3hours 30 minutes
Time taken by the bus to complete the remaining 350
= 350/60 = 55/6 hrs = 5 hours 50 minutes
Matatu waits for 5hr 50min – 3hr 30 min = 2 hrs 20 min
7. Total distance = 100 + 140 + 150 = 490
Total speed = 88 + 164 = 252 km/hr
252 km/hr into m/h = 252 x 1000 = 70m/h
3600
Time taken = 490/70 = 7 sec
8. Distance = (5 + 15)m = 20m = 0.02km
S ⇒ Bus = 40 km/h
Trailer = xkm/h
Relative speed = (40 – x) km/h
T = 4.8 sec. = 4.8h
3600
S = D
T
(40 – x) = 0.02
48
3600
≃
0.02 x 3600
48
= 15 km/h
40 – x = 15
x = 25 km/h
9. L.C.M = 24 x
32 x
53 = 1800
GC.D. = 2 x 3 x 52 = 150
10. Total distance = 60 cm
Total time taken = 3 1/5 hrs
Let speed in still water be x km/h
Speed upstream = (x – 5) km/h
Speed downstream = (x + 5) km/h
30 + 30 = 16
x – 5 x + 5 5
30x – 150 + 30x + 150 = 16 (x2 – 25)
5
300x = 16x2 – 400
x= –5/4 or 20
Speed in still water is 20 km/hr
11. When David left, Ojwang had covered 15 x 3/2 = 22.5 km.
a) (i) Remaining dist. = 40 – 22.5 = 17.5 km
Relative speed = 15 + 25 = 40 km/h
Time taken before meeting = 17.5 = 0.4375 hrs
40
Ojwang covered 15 x 0.437 = 5.5625 km
Distance from Ojwang’s house = 22.5 + 6.5625 √
= 29.0625 km
(ii) 0.4375 = 26 min 15 sec
They met at 10.30 + 26.15
= 10.56. 15 am.
(iii) 40 – 29.0625 √ = 10.9375 km√
b) Time take = 10.9375
√ = 0.9115 hrs
12
= 54 min, 41 sec.
They arrived at 10.56. 15 + 54.41 + 10 min
= 12.00. 56 pm. √
12. (a) In 10minutes Kamau has travelled
10 x 24 = 6km
60
Distance left = 42 – 6 = 36km
Relating speed = 24 + 50.4k/hr
= 74.4km/hr
Time taken to meet = 42 = 0.565hrs
74.4
= 34minutes
Time for meeting is 6.10
34
6.44a.m
34 x 50.4 = 28.56km from R or 13.44 from S
60
(b) Kamau arrival time
42km = 1.75hrs
24km/hr 1hr .45 minutes
6.00a.m
1.45
7.45a.m
(c) Mrs Ronoh speed = D
T
= 50.4km/hr
Twice = 50.4 x 2 = 100.8
7.00a.m, Mr. Kamau covered = 1×24= 24km
Retain speed = 100.8- 24 = 76.8km/hr
So 24 = 8.75
76.8
He was overtaken at 7.00
+ 18.75
7.18am
At distance of D = S x t
= 100.8 x 189.75
60
31.5km from S or 10.5km from R
13. i) A gains on B at the rate of (72 – 56) Km/hr or 16km/h
჻ in 1 hr A gains on B 16km
In 545 A gains on B
16 X 1000 X 54 m = 240
60 X 60
The sum of the lengths of the two trains is 240m but the length of the first train is 100m
The length of the second train is 140m
ii) Relative speed = (72 + 56) km/h = 128km/hr
Distance between A and B decrease at the rate of 128km/hr
The distance decreases by 240m
60 X 60 X 240 s = 27 seconds
128 X 1000 4
= 6 ¾ s
14. (a) Time = D
S
= 5
x hrs
(ii) Time = 7
x + 24 hrs
(b) 5 – 36 = 7
x 60 x + 24
7 = 25 – 3x
x + 24 5x
35x = 25x – 3x2 + 600 – 72x
3x2 + 82x – 600 = 0
(3x + 100) (x-6) = 0
x = -100 or 6
3
His speed = 6km/hr
(c) Time = S x T
= 5 x 60
6
= 50mins
15. a) Relative speed = 80 – 60
= 20 km/h
Time = 40 hrs
20
= 2 hrs
(b) 1.50 p.m. = 13.50 hrs.
Time = 13.50 + 2 = 15.50 hrs
16. (a) Nairobi 400km Kisumu
Speed = 120km/h
Distance = 400km
Time taken = 400 = 10 = 3hrs 20min
120
8.30 + 3hrs 20min = 11:50a.m
(b) at 8.30a.m distance covered by bus = ½ x 80 = 40km
Dist. Left = 360km speed = 200km/h
Time taken = 360 = 1hr 48mins
200
They met at 8:30+ 1hr 48mins
= 10:18a.m
(c) 8 – 10.18a.m is 2hrs 18mins distance = 2 x 80 +18 x 80
60
= 160 + 24km = 184 from Nairobi
(d) car arrived in Nairobi after 3hrs 20mins
Bus traveled a time of 3hrs 20mins + 30mins
3hrs 50mins
Dist. = 3 x 80 + 50 x 80 = 240 + 66 2/3
60
Distance from Kisumu = 93 1/3 km
17. Total distance = 25m
Relative speed= 54km/hr
To m/s = 54 x 1000 = 15/ms
60 x 60
Time they met = 25
15
= 12/3 sec
