Relative Motion
Q. A cyclist is moving at 15 m/s and a pedestrian is walking at 5 m/s in the same direction. What is the relative speed of the pedestrian with respect to the cyclist?
A.
10 m/s
B.
5 m/s
C.
20 m/s
D.
15 m/s
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Solution
Relative speed = Speed of pedestrian - Speed of cyclist = 5 m/s - 15 m/s = -10 m/s (10 m/s behind).
Correct Answer: A — 10 m/s
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Q. A cyclist is moving at 15 m/s and passes a stationary observer. If the observer starts moving at 5 m/s in the same direction, what is the speed of the cyclist relative to the observer?
A.
10 m/s
B.
15 m/s
C.
20 m/s
D.
5 m/s
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Solution
Relative speed = Speed of cyclist - Speed of observer = 15 m/s - 5 m/s = 10 m/s.
Correct Answer: A — 10 m/s
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Q. A cyclist is moving at 15 m/s towards the east while a car is moving at 25 m/s towards the west. What is the relative speed of the cyclist with respect to the car?
A.
10 m/s
B.
15 m/s
C.
40 m/s
D.
25 m/s
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Solution
Relative speed = Speed of cyclist + Speed of car = 15 m/s + 25 m/s = 40 m/s.
Correct Answer: C — 40 m/s
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Q. A cyclist is moving at 15 m/s while a car is moving at 25 m/s in the same direction. What is the speed of the cyclist relative to the car?
A.
10 m/s
B.
15 m/s
C.
25 m/s
D.
40 m/s
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Solution
Relative speed = Speed of car - Speed of cyclist = 25 m/s - 15 m/s = 10 m/s.
Correct Answer: A — 10 m/s
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Q. A cyclist is moving at a speed of 15 km/h. If a car is moving in the same direction at 30 km/h, what is the relative speed of the car with respect to the cyclist?
A.
15 km/h
B.
30 km/h
C.
45 km/h
D.
0 km/h
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Solution
Relative speed = speed of car - speed of cyclist = 30 - 15 = 15 km/h.
Correct Answer: A — 15 km/h
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Q. A cyclist travels at a speed of 15 km/h. If he encounters a headwind of 5 km/h, what is his effective speed?
A.
10 km/h
B.
15 km/h
C.
20 km/h
D.
25 km/h
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Solution
Effective speed = speed of cyclist - speed of wind = 15 - 5 = 10 km/h.
Correct Answer: A — 10 km/h
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Q. A man can run at 5 km/h in still air. If he runs in a direction opposite to the wind blowing at 3 km/h, what is his effective speed?
A.
2 km/h
B.
5 km/h
C.
8 km/h
D.
3 km/h
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Solution
Effective speed = speed of man - speed of wind = 5 - 3 = 2 km/h.
Correct Answer: A — 2 km/h
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Q. A man can run at a speed of 5 m/s in still air. If he runs in a direction opposite to the wind blowing at 2 m/s, what is his effective speed?
A.
3 m/s
B.
5 m/s
C.
7 m/s
D.
10 m/s
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Solution
Effective speed = speed of man - speed of wind = 5 - 2 = 3 m/s.
Correct Answer: A — 3 m/s
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Q. A man can walk at a speed of 5 km/h. If he walks in a direction opposite to the wind blowing at 3 km/h, what is his effective speed?
A.
2 km/h
B.
5 km/h
C.
8 km/h
D.
3 km/h
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Solution
Effective speed = speed of man + speed of wind = 5 + 3 = 8 km/h.
Correct Answer: C — 8 km/h
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Q. A person is running at 3 m/s on a moving escalator that moves at 2 m/s in the same direction. What is the speed of the person relative to a stationary observer?
A.
1 m/s
B.
3 m/s
C.
5 m/s
D.
2 m/s
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Solution
Speed of person relative to observer = Speed of escalator + Speed of person = 2 m/s + 3 m/s = 5 m/s.
Correct Answer: C — 5 m/s
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Q. A person is running at 8 m/s in a train moving at 12 m/s in the same direction. What is the speed of the person relative to the ground?
A.
4 m/s
B.
8 m/s
C.
12 m/s
D.
20 m/s
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Solution
Speed of person relative to ground = Speed of train + Speed of person = 12 m/s + 8 m/s = 20 m/s.
Correct Answer: D — 20 m/s
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Q. A person is running at 8 m/s on a moving walkway that moves at 2 m/s in the same direction. What is the speed of the person relative to the ground?
A.
6 m/s
B.
8 m/s
C.
10 m/s
D.
12 m/s
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Solution
Speed relative to ground = Speed of person + Speed of walkway = 8 m/s + 2 m/s = 10 m/s.
Correct Answer: C — 10 m/s
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Q. A person is running at a speed of 10 m/s. If he is running towards a train moving at 20 m/s in the opposite direction, what is the relative speed of the train with respect to the person?
A.
10 m/s
B.
20 m/s
C.
30 m/s
D.
40 m/s
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Solution
Relative speed = speed of train + speed of person = 20 + 10 = 30 m/s.
Correct Answer: C — 30 m/s
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Q. A person is walking at 2 m/s on a train moving at 10 m/s. What is the speed of the person relative to the ground?
A.
2 m/s
B.
8 m/s
C.
10 m/s
D.
12 m/s
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Solution
Speed of person relative to ground = Speed of train + Speed of person = 10 m/s + 2 m/s = 12 m/s.
Correct Answer: D — 12 m/s
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Q. A person is walking at 4 km/h in a train moving at 36 km/h. What is the speed of the person relative to the ground?
A.
32 km/h
B.
40 km/h
C.
36 km/h
D.
4 km/h
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Solution
Speed of person relative to ground = Speed of train + Speed of person = 36 km/h + 4 km/h = 40 km/h.
Correct Answer: B — 40 km/h
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Q. A person walks at 4 km/h and runs at 10 km/h. If he walks for 30 minutes and then runs for 30 minutes, how far does he travel?
A.
5 km
B.
7 km
C.
8 km
D.
10 km
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Solution
Distance walked = 4 km/h * 0.5 h = 2 km. Distance run = 10 km/h * 0.5 h = 5 km. Total distance = 2 + 5 = 7 km.
Correct Answer: C — 8 km
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Q. A person walks at 4 km/h and runs at 10 km/h. If he walks for 30 minutes and then runs for 30 minutes, what is his average speed?
A.
6 km/h
B.
7 km/h
C.
8 km/h
D.
9 km/h
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Solution
Total distance = (4 × 0.5) + (10 × 0.5) = 2 + 5 = 7 km. Total time = 1 hour. Average speed = 7 km/h.
Correct Answer: B — 7 km/h
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Q. A person walks at 4 km/h and runs at 10 km/h. If he walks for 30 minutes and then runs for 1 hour, how far does he travel?
A.
7 km
B.
8 km
C.
9 km
D.
10 km
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Solution
Distance walked = 4 * 0.5 = 2 km; Distance run = 10 * 1 = 10 km; Total distance = 2 + 10 = 12 km.
Correct Answer: C — 9 km
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Q. A person walks at 4 km/h in a train moving at 36 km/h. What is the speed of the person relative to the ground?
A.
32 km/h
B.
36 km/h
C.
40 km/h
D.
4 km/h
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Solution
Speed of person relative to ground = Speed of train + Speed of person = 36 km/h + 4 km/h = 40 km/h.
Correct Answer: C — 40 km/h
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Q. A person walks at 4 km/h in a train moving at 60 km/h. What is the speed of the person relative to the ground?
A.
64 km/h
B.
60 km/h
C.
4 km/h
D.
56 km/h
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Solution
Speed of person relative to ground = Speed of train + Speed of person = 60 km/h + 4 km/h = 64 km/h.
Correct Answer: A — 64 km/h
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Q. A person walks at 4 km/h in still water. If the current of the river is 2 km/h, what is the speed of the person relative to the bank when walking upstream?
A.
2 km/h
B.
4 km/h
C.
6 km/h
D.
8 km/h
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Solution
Speed upstream = Speed of person - Speed of current = 4 km/h - 2 km/h = 2 km/h.
Correct Answer: A — 2 km/h
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Q. A person walks at 4 km/h on a moving escalator that moves at 2 km/h. What is the speed of the person relative to a stationary observer?
A.
2 km/h
B.
4 km/h
C.
6 km/h
D.
8 km/h
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Solution
Speed of person relative to observer = Speed of person + Speed of escalator = 4 km/h + 2 km/h = 6 km/h.
Correct Answer: C — 6 km/h
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Q. A plane is flying at 200 m/s in still air. If there is a headwind of 50 m/s, what is the speed of the plane relative to the ground?
A.
150 m/s
B.
200 m/s
C.
250 m/s
D.
300 m/s
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Solution
Speed relative to ground = Speed of plane - Speed of wind = 200 m/s - 50 m/s = 150 m/s.
Correct Answer: A — 150 m/s
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Q. A swimmer can swim at 3 km/h in still water. If he swims across a river flowing at 2 km/h, what is his resultant speed?
A.
3 km/h
B.
4 km/h
C.
5 km/h
D.
6 km/h
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Solution
Resultant speed = √(3² + 2²) = √(9 + 4) = √13 ≈ 3.6 km/h.
Correct Answer: C — 5 km/h
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Q. A swimmer can swim at 3 m/s in still water. If the river flows at 1 m/s, what is the swimmer's speed when swimming across the river?
A.
2 m/s
B.
3 m/s
C.
4 m/s
D.
5 m/s
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Solution
Speed across the river = √(3^2 - 1^2) = √(9 - 1) = √8 = 2.83 m/s (approximately 2 m/s).
Correct Answer: A — 2 m/s
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Q. A swimmer can swim at 3 m/s in still water. If the river flows at 2 m/s, what is the swimmer's speed relative to the bank when swimming upstream?
A.
1 m/s
B.
2 m/s
C.
3 m/s
D.
5 m/s
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Solution
Speed relative to bank = Speed of swimmer - Speed of river = 3 m/s - 2 m/s = 1 m/s.
Correct Answer: A — 1 m/s
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Q. A swimmer can swim at 4 km/h in still water. If he swims across a river that is 1 km wide and the current is 2 km/h, how long will it take him to reach the opposite bank?
A.
15 minutes
B.
30 minutes
C.
45 minutes
D.
1 hour
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Solution
Time = distance/speed = 1 km / 4 km/h = 0.25 hours = 15 minutes.
Correct Answer: B — 30 minutes
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Q. A train is moving at 72 km/h and a bird flies in the opposite direction at 18 km/h. What is the speed of the bird relative to the train?
A.
54 km/h
B.
72 km/h
C.
90 km/h
D.
18 km/h
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Solution
Relative speed = Speed of train + Speed of bird = 72 km/h + 18 km/h = 90 km/h.
Correct Answer: A — 54 km/h
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Q. A train is moving at 72 km/h and passes a platform in 20 seconds. What is the length of the platform if the train is 180 meters long?
A.
200 m
B.
300 m
C.
400 m
D.
500 m
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Solution
Speed of train = 72 km/h = 20 m/s. Time = 20 s. Distance = Speed × Time = 20 m/s × 20 s = 400 m. Length of platform = 400 m - 180 m = 220 m.
Correct Answer: B — 300 m
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Q. A train is moving at 72 km/h and passes a platform in 20 seconds. What is the length of the train?
A.
100 m
B.
200 m
C.
300 m
D.
400 m
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Solution
Length of train = Speed × Time = (72 km/h × (1000 m/1 km) / (3600 s/1 h)) × 20 s = 400 m.
Correct Answer: B — 200 m
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