Relative Motion
Q. A train is moving at 72 km/h and passes a platform in 30 seconds. What is the length of the platform if the train is 200 meters long?
A.
200 m
B.
300 m
C.
400 m
D.
500 m
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Solution
Speed in m/s = 72 * (1000/3600) = 20 m/s. Distance = Speed × Time = 20 m/s × 30 s = 600 m. Length of platform = 600 m - 200 m = 400 m.
Correct Answer: B — 300 m
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Q. A train is moving at 90 km/h and a bird flies at 45 km/h in the opposite direction. What is the speed of the bird relative to the train?
A.
135 km/h
B.
45 km/h
C.
90 km/h
D.
135 km/h
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Solution
Relative speed = Speed of train + Speed of bird = 90 km/h + 45 km/h = 135 km/h.
Correct Answer: A — 135 km/h
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Q. A train leaves a station and travels at 90 km/h. Another train leaves the same station 30 minutes later and travels at 120 km/h. How far from the station will they meet?
A.
90 km
B.
120 km
C.
150 km
D.
180 km
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Solution
Let the distance be d. Time taken by first train = d/90. Time taken by second train = d/120. Setting up the equation gives d = 150 km.
Correct Answer: C — 150 km
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Q. A train leaves a station at 70 km/h. Another train leaves the same station 30 minutes later at 90 km/h. How far from the station will they meet?
A.
70 km
B.
90 km
C.
100 km
D.
110 km
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Solution
Let the distance be d. Time taken by first train = d/70, second train = d/90. They meet when d/70 = d/90 + 0.5. Solving gives d = 100 km.
Correct Answer: C — 100 km
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Q. A train leaves a station at 80 km/h and another train leaves the same station 30 minutes later at 100 km/h. How far from the station will they meet?
A.
100 km
B.
120 km
C.
150 km
D.
180 km
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Solution
Let the time taken by the first train be t hours. Distance = speed * time. 80t = 100(t - 0.5). Solving gives t = 2 hours, so distance = 80 * 2 = 160 km.
Correct Answer: B — 120 km
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Q. A train moving at 72 km/h overtakes a man walking at 6 km/h in the same direction. How fast does the train appear to be moving to the man?
A.
66 km/h
B.
72 km/h
C.
78 km/h
D.
84 km/h
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Solution
Relative speed = Speed of train - Speed of man = 72 km/h - 6 km/h = 66 km/h.
Correct Answer: A — 66 km/h
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Q. A train moving at 72 km/h passes a man walking at 6 km/h in the same direction. How fast does the train appear to be moving to the man?
A.
66 km/h
B.
72 km/h
C.
78 km/h
D.
84 km/h
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Solution
Relative speed = Speed of train - Speed of man = 72 km/h - 6 km/h = 66 km/h.
Correct Answer: A — 66 km/h
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Q. A train moving at 72 km/h passes a platform 300 m long. How long does it take to cross the platform completely?
A.
10 seconds
B.
15 seconds
C.
20 seconds
D.
25 seconds
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Solution
Total distance = Length of train + Length of platform. If length of train is L, time = (L + 300)/20 m/s. Assuming L = 300 m, time = (300 + 300)/20 = 30 seconds.
Correct Answer: B — 15 seconds
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Q. A train travels at a speed of 72 km/h. How far will it travel in 30 minutes?
A.
12 km
B.
18 km
C.
24 km
D.
36 km
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Solution
Distance = speed × time = 72 km/h × 0.5 h = 36 km.
Correct Answer: B — 18 km
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Q. A train travels at a speed of 90 km/h and a car at 60 km/h. If they start from the same point and travel in the same direction, how far apart will they be after 1 hour?
A.
30 km
B.
20 km
C.
10 km
D.
40 km
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Solution
Relative speed = 90 - 60 = 30 km/h. Distance apart after 1 hour = 30 km.
Correct Answer: A — 30 km
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Q. If a boat can travel 20 km upstream in 4 hours, what is the speed of the current if the speed of the boat in still water is 10 km/h?
A.
2 km/h
B.
3 km/h
C.
4 km/h
D.
5 km/h
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Solution
Speed upstream = distance/time = 20/4 = 5 km/h. Speed of current = speed of boat - speed upstream = 10 - 5 = 5 km/h.
Correct Answer: A — 2 km/h
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Q. If a boat can travel at 15 km/h in still water and the current is 5 km/h, what is the speed of the boat upstream?
A.
10 km/h
B.
15 km/h
C.
20 km/h
D.
25 km/h
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Solution
Speed upstream = speed of boat - speed of current = 15 - 5 = 10 km/h.
Correct Answer: A — 10 km/h
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Q. If a car travels at a speed of 80 km/h and a bike travels at 60 km/h, how far apart will they be after 1 hour if they start from the same point and travel in the same direction?
A.
20 km
B.
30 km
C.
40 km
D.
50 km
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Solution
Relative speed = 80 - 60 = 20 km/h. Distance apart after 1 hour = 20 km.
Correct Answer: A — 20 km
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Q. If a cyclist travels at 15 km/h and a pedestrian walks at 5 km/h, how much faster is the cyclist than the pedestrian?
A.
5 km/h
B.
10 km/h
C.
15 km/h
D.
20 km/h
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Solution
Difference in speed = 15 - 5 = 10 km/h.
Correct Answer: B — 10 km/h
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Q. If two cars are moving in opposite directions at speeds of 40 km/h and 60 km/h, what is their relative speed?
A.
100 km/h
B.
20 km/h
C.
40 km/h
D.
60 km/h
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Solution
Relative speed = Speed of car 1 + Speed of car 2 = 40 km/h + 60 km/h = 100 km/h.
Correct Answer: A — 100 km/h
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Q. If two cars are moving towards each other at speeds of 40 km/h and 60 km/h, how long will it take for them to meet if they are 200 km apart?
A.
1 hour
B.
2 hours
C.
3 hours
D.
4 hours
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Solution
Relative speed = 40 km/h + 60 km/h = 100 km/h. Time = Distance / Relative Speed = 200 km / 100 km/h = 2 hours.
Correct Answer: B — 2 hours
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Q. If two objects are moving in opposite directions with speeds of 10 m/s and 15 m/s, what is their relative speed?
A.
5 m/s
B.
25 m/s
C.
15 m/s
D.
10 m/s
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Solution
Relative speed = Speed of object 1 + Speed of object 2 = 10 m/s + 15 m/s = 25 m/s.
Correct Answer: B — 25 m/s
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Q. If two objects are moving in opposite directions with speeds of 20 m/s and 30 m/s, what is their relative velocity?
A.
10 m/s
B.
50 m/s
C.
20 m/s
D.
30 m/s
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Solution
Relative velocity = Speed of object 1 + Speed of object 2 = 20 m/s + 30 m/s = 50 m/s.
Correct Answer: B — 50 m/s
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Q. If two objects are moving in opposite directions with speeds of 40 m/s and 60 m/s, what is their relative speed?
A.
20 m/s
B.
40 m/s
C.
60 m/s
D.
100 m/s
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Solution
Relative speed = Speed of object 1 + Speed of object 2 = 40 m/s + 60 m/s = 100 m/s.
Correct Answer: D — 100 m/s
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Q. If two objects are moving towards each other with speeds of 40 m/s and 60 m/s, how long will it take for them to collide if they are 200 m apart?
A.
1 s
B.
2 s
C.
3 s
D.
4 s
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Solution
Relative speed = 40 m/s + 60 m/s = 100 m/s. Time = Distance / Relative speed = 200 m / 100 m/s = 2 s.
Correct Answer: B — 2 s
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Q. Two cars are moving towards each other at speeds of 50 km/h and 70 km/h. If they are 200 meters apart, how long will it take for them to meet?
A.
5 seconds
B.
10 seconds
C.
15 seconds
D.
20 seconds
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Solution
Relative speed = 50 km/h + 70 km/h = 120 km/h = 33.33 m/s. Time = Distance/Speed = 200 m / 33.33 m/s = 6 seconds.
Correct Answer: B — 10 seconds
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Q. Two cars are moving towards each other with speeds of 50 km/h and 70 km/h. How long will it take for them to collide if they are 200 meters apart?
A.
5 seconds
B.
10 seconds
C.
15 seconds
D.
20 seconds
Show solution
Solution
Relative speed = 50 km/h + 70 km/h = 120 km/h = 33.33 m/s. Time = Distance / Relative speed = 200 m / 33.33 m/s = 6 seconds.
Correct Answer: B — 10 seconds
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Q. Two cars start from the same point and travel in opposite directions at speeds of 70 km/h and 50 km/h. How far apart will they be after 2 hours?
A.
240 km
B.
220 km
C.
200 km
D.
180 km
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Solution
Relative speed = 70 + 50 = 120 km/h. Distance apart after 2 hours = 120 × 2 = 240 km.
Correct Answer: A — 240 km
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Q. Two cars start from the same point and travel in opposite directions. If car A travels at 40 km/h and car B at 60 km/h, how far apart will they be after 1 hour?
A.
50 km
B.
80 km
C.
100 km
D.
120 km
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Solution
Relative speed = 40 + 60 = 100 km/h. Distance apart after 1 hour = 100 km.
Correct Answer: B — 80 km
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Q. Two cars start from the same point and travel in opposite directions. If car A travels at 70 km/h and car B at 50 km/h, how far apart will they be after 2 hours?
A.
240 km
B.
220 km
C.
200 km
D.
180 km
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Solution
Relative speed = 70 + 50 = 120 km/h. Distance apart after 2 hours = 120 * 2 = 240 km.
Correct Answer: A — 240 km
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Q. Two cyclists start from the same point and ride in opposite directions at speeds of 12 km/h and 15 km/h. How far apart will they be after 2 hours?
A.
54 km
B.
60 km
C.
30 km
D.
42 km
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Solution
Relative speed = 12 + 15 = 27 km/h. Distance apart after 2 hours = 27 * 2 = 54 km.
Correct Answer: B — 60 km
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Q. Two cyclists start from the same point and ride in opposite directions at speeds of 15 km/h and 20 km/h. How far apart will they be after 1 hour?
A.
25 km
B.
30 km
C.
35 km
D.
40 km
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Solution
Distance apart = (15 + 20) * 1 = 35 km.
Correct Answer: B — 30 km
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Q. Two observers are moving towards each other at speeds of 20 m/s and 30 m/s. What is the relative velocity of one observer as seen by the other?
A.
10 m/s
B.
20 m/s
C.
50 m/s
D.
60 m/s
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Solution
Relative velocity = Velocity of observer 1 + Velocity of observer 2 = 20 m/s + 30 m/s = 50 m/s.
Correct Answer: C — 50 m/s
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Q. Two observers are moving towards each other at speeds of 20 m/s and 30 m/s. What is the relative velocity of one observer with respect to the other?
A.
10 m/s
B.
20 m/s
C.
50 m/s
D.
60 m/s
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Solution
Relative velocity = Velocity of observer 1 + Velocity of observer 2 = 20 m/s + 30 m/s = 50 m/s.
Correct Answer: C — 50 m/s
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Q. Two observers are moving towards each other at speeds of 20 m/s and 30 m/s. What is the speed of one observer as seen by the other?
A.
10 m/s
B.
20 m/s
C.
50 m/s
D.
60 m/s
Show solution
Solution
Relative speed = Speed of observer 1 + Speed of observer 2 = 20 m/s + 30 m/s = 50 m/s.
Correct Answer: C — 50 m/s
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