Quiz: Relative Speed Fundamentals
Relative speed is the rate at which the distance between two objects changes. It is the foundation of many competitive-exam problems involving trains, cars, boats, and even a stationary observer.
This quiz tests the core ideas from Lesson 4: Relative Speed: Basics:
- Same direction: relative speed is the difference of the speeds.
- Opposite direction: relative speed is the sum of the speeds.
- Stationary object: relative speed equals the moving object’s own speed.
- Basic problems: time to meet, time to overtake, and distance covered using relative speed.
Use the relation Time = Distance ÷ Relative Speed throughout. All questions are of medium difficulty and are answerable from the lesson alone.
Q1. Two cars move in the same direction at ##60## km/h and ##40## km/h. What is their relative speed?
For motion in the same direction, relative speed is the difference: ##60 - 40 = 20## km/h.
Q2. Two trains approach each other on parallel tracks at ##50## km/h and ##30## km/h. Their relative speed is:
For motion in opposite directions, relative speed is the sum: ##50 + 30 = 80## km/h.
Q3. A man walks at ##5## km/h past a stationary tree. What is his speed relative to the tree?
A stationary object has zero speed, so relative speed equals the moving object's speed: ##5## km/h.
Q4. Two cyclists ride in the same direction at ##18## km/h and ##12## km/h. How long does the faster take to gain ##3## km on the slower?
Relative speed ##= 18 - 12 = 6## km/h. Time ##= \dfrac{3}{6} = 0.5## h ##= 30## minutes.
Q5. Two trains ##200## m apart move towards each other at ##20## m/s and ##30## m/s. How long until they meet?
Relative speed ##= 20 + 30 = 50## m/s. Time ##= \dfrac{200}{50} = 4## s.
Q6. When two bodies move in the same direction, their relative speed is:
Same-direction motion gives relative speed equal to the difference of the speeds.
Q7. When two bodies move in opposite directions, their relative speed is:
Opposite-direction motion gives relative speed equal to the sum of the speeds.
Q8. A car at ##72## km/h passes a stationary pole. What is the car's speed relative to the pole in m/s?
Relative speed to a stationary object is the car's own speed: ##72 \times \dfrac{5}{18} = 20## m/s.
Q9. Two runners move in the same direction at ##8## m/s and ##6## m/s. What is the rate at which the gap between them changes?
Same direction: relative speed ##= 8 - 6 = 2## m/s, the rate the gap changes.
Q10. Two buses ##120## km apart travel towards each other at ##50## km/h and ##70## km/h. After how long do they meet?
Relative speed ##= 50 + 70 = 120## km/h. Time ##= \dfrac{120}{120} = 1## hour.
Q11. A thief runs at ##10## m/s and a policeman chases at ##12## m/s. What is the relative speed of the policeman with respect to the thief?
Both move in the same direction, so relative speed ##= 12 - 10 = 2## m/s.
Q12. Two trains of length ##100## m each move in opposite directions at ##15## m/s and ##10## m/s. How long do they take to cross each other completely?
Total distance ##= 100 + 100 = 200## m. Relative speed ##= 15 + 10 = 25## m/s. Time ##= \dfrac{200}{25} = 8## s.
Q13. A boat moves at ##12## km/h and a raft drifts at ##4## km/h in the same direction. What is the boat's speed relative to the raft?
Same direction: relative speed ##= 12 - 4 = 8## km/h.
Q14. Two objects move in opposite directions at ##25## m/s and ##15## m/s. What is their relative speed?
Opposite directions: relative speed ##= 25 + 15 = 40## m/s.
Q15. A train ##150## m long at ##20## m/s passes a stationary platform ##250## m long. How long does it take?
Relative speed to the stationary platform is ##20## m/s. Distance ##= 150 + 250 = 400## m. Time ##= \dfrac{400}{20} = 20## s.
Q16. Two cars start from the same point in opposite directions at ##45## km/h and ##35## km/h. How far apart are they after ##2## hours?
Relative speed ##= 45 + 35 = 80## km/h. Distance ##= 80 \times 2 = 160## km.
Q17. A cyclist at ##15## km/h is chased by a motorcyclist at ##45## km/h. The gap between them is ##6## km. How long until the motorcyclist catches up?
Relative speed ##= 45 - 15 = 30## km/h. Time ##= \dfrac{6}{30} = 0.2## h ##= 12## minutes.
Q18. Two trains ##300## m apart move in the same direction at ##25## m/s and ##15## m/s. How long until the faster catches the slower?
Relative speed ##= 25 - 15 = 10## m/s. Time ##= \dfrac{300}{10} = 30## s.
Q19. If two objects move in opposite directions, the distance between them changes at a rate equal to:
In opposite directions the gap grows (or shrinks) at the sum of the speeds.
Q20. Two trains ##180## m apart approach each other at ##12## m/s and ##18## m/s. How long until they meet?
Relative speed ##= 12 + 18 = 30## m/s. Time ##= \dfrac{180}{30} = 6## s.