Practice Questions
Concept Explanation
Relative speed is the speed of one moving object as seen from another moving object.
Key Formulas
- Same direction: relative speed = |a − b|
- Opposite direction: relative speed = a + b
- Time to meet or cross = Total distance / Relative speed
Example
Two cars at 60 km/h and 40 km/h approach each other. Relative speed = 60 + 40 = 100 km/h.
Common Trap
Subtract speeds only when moving in the same direction. Add when moving toward each other.
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Q1 EasyTwo cars travel toward each other at speeds of 60 km/h and 40 km/h respectively. What is their relative speed?ExplanationOpposite direction: relative speed = 60 + 40 = 100 km/h.
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Q2 EasyTwo vehicles move in the same direction at 90 km/h and 60 km/h respectively. What is their relative speed?ExplanationSame direction: relative speed = |90 − 60| = 30 km/h.
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Q3 EasyTwo runners move in the same direction at 12 m/s and 8 m/s respectively. At what rate does the faster runner gain on the slower runner?ExplanationRelative speed = 12 − 8 = 4 m/s.
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Q4 EasyTwo trains, each moving at 72 km/h, travel toward each other on parallel tracks. What is their relative speed?ExplanationOpposite direction: relative speed = 72 + 72 = 144 km/h.
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Q5 EasyTwo boats move in the same direction at 15 km/h and 10 km/h respectively. What is their relative speed?ExplanationSame direction: relative speed = 15 − 10 = 5 km/h.
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Q6 EasyTwo cars travel toward each other at 55 km/h and 65 km/h respectively. What is their relative speed?ExplanationOpposite direction: relative speed = 55 + 65 = 120 km/h.
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Q7 EasyTwo vehicles move in the same direction at 100 km/h and 70 km/h respectively. At what rate does the gap between them close?ExplanationRelative speed = 100 − 70 = 30 km/h.
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Q8 MediumTwo persons A and B move toward each other at 50 km/h and 30 km/h respectively. If they meet after 2 hours, what was the initial distance between them?ExplanationRelative speed = 80 km/h. Initial gap = 80 × 2 = 160 km.
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Q9 MediumCar A travels at 80 km/h and chases Car B, which moves at 60 km/h in the same direction. If B is 40 km ahead of A, after how many hours will A catch B?ExplanationRelative speed = 20 km/h. Time = 40 ÷ 20 = 2 hours.
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Q10 MediumTwo cyclists start from opposite ends of a 210 km route and ride toward each other at 18 km/h and 24 km/h respectively. After how many hours will they meet?ExplanationRelative speed = 42 km/h. Time = 210 ÷ 42 = 5 hours.
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Q11 MediumTwo objects move toward each other, each at 45 km/h. If the initial distance between them is 225 km, after how many hours will they meet?ExplanationRelative speed = 90 km/h. Time = 225 ÷ 90 = 2.5 hours.
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Q12 MediumTwo trains are 300 km apart and move toward each other at 50 km/h and 70 km/h respectively. After how many hours will they meet?ExplanationRelative speed = 120 km/h. Time = 300 ÷ 120 = 2.5 hours.
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Q13 HardObject A moves at 20 m/s and Object B at 14 m/s in the same direction. If A is 60 m behind B, how many seconds will A take to catch B?ExplanationRelative speed = 6 m/s. Time = 60 ÷ 6 = 10 s.
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Q14 HardWhich pair of speeds gives a relative speed of 50 km/h when both objects move in the same direction?Explanation|80 − 30| = 50 km/h.
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DS1 Easy
What is the relative speed of the two objects?
Statement ITwo objects move toward each other at speeds of 60 km/h and 40 km/h respectively.
Statement IITwo objects move in the same direction at speeds of 60 km/h and 40 km/h respectively.
ExplanationStatement I alone: 60 + 40 = 100 km/h. Statement II alone: 60 − 40 = 20 km/h. -
DS2 Easy
After how many hours will the two objects meet?
Statement IThe initial distance between them is 160 km.
Statement IITheir relative speed is 80 km/h.
ExplanationBoth statements are needed: time = 160 ÷ 80 = 2 hours.
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DS3 Easy
What was the initial distance between the two objects?
Statement IThey meet after 2 hours.
Statement IITheir relative speed is 50 km/h.
ExplanationBoth statements are needed: distance = 50 × 2 = 100 km. -
DS4 Medium
Is the relative speed of the two objects greater than 100 km/h?
Statement IThe objects move toward each other at 55 km/h and 65 km/h respectively.
Statement IIThe objects move in the same direction at 90 km/h and 60 km/h respectively.
ExplanationStatement I alone: 120 km/h > 100. Statement II alone: 30 km/h, which is not sufficient.