Practice Questions
Concept Explanation
Mixed motion combines several ideas — average speed, relative speed, trains, boats, or multi-leg journeys — in one problem.
Key Formulas
- Average speed = Total distance / Total time
- Relative speed: same direction |a − b|, opposite a + b
- Break complex trips into legs; keep units consistent
Example
A car goes 120 km at 60 km/h and returns at 40 km/h. Total 240 km in 5 h. Average speed = 48 km/h.
Common Trap
Do not average leg speeds unless equal times or use the correct harmonic mean for equal distances.
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Q1 Medium
A car travels 120 km at 60 km/h and returns over the same route at 40 km/h. What is the average speed for the entire round trip?
ExplanationTotal 240 km in 5 h. Average = 48 km/h. -
Q2 Medium
A person walks 6 km at 4 km/h and then runs 6 km at 12 km/h. What is the average speed for the entire journey of 12 km?
ExplanationTotal 12 km in 1.5 + 0.5 = 2 h. Average = 6 km/h. -
Q3 Easy
Two trains start from stations 200 km apart and move toward each other at 50 km/h and 70 km/h respectively. After how many hours will they meet?
ExplanationTime = 200/120 = 1.67 hours. -
Q4 Hard
A boat can travel at 12 km/h in still water and the speed of the stream is 3 km/h. The boat goes 30 km downstream and then returns 30 km upstream. What is the total time for the journey?
ExplanationDown 30/15 = 2 h; up 30/9 = 3.33 h. Total = 5.33 h. -
Q5 Hard
A train 120 metres long crosses a pole at 54 km/h while another train 180 metres long crosses a pole at 72 km/h. How long does each train take to cross its pole?
Explanation54 km/h = 15 m/s: 120/15 = 8 s. 72 km/h = 20 m/s: 180/20 = 9 s. -
Q6 Hard
A vehicle covers 100 km at 50 km/h and then 50 km at 25 km/h. What is the average speed for the entire journey of 150 km?
ExplanationTime = 2 + 2 = 4 h. Average = 150/4 = 37.5 km/h. -
Q7 Medium
A car travels 60 km at 30 km/h and then another 60 km at 60 km/h. What is the average speed for the entire journey of 120 km?
ExplanationTotal 120 km in 2 + 1 = 3 h. Average = 40 km/h.
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Q8 Easy
Car A moving at 80 km/h and car B moving at 60 km/h start from two points 100 km apart and travel toward each other. After how many hours will they meet?
ExplanationTime = 100/140 ≈ 0.71 hours. -
Q9 Easy
A runner moving at 8 m/s chases another runner moving at 6 m/s on a straight track. The slower runner is 40 metres ahead. After how many seconds will the faster runner catch up?
ExplanationRelative = 2 m/s. Time = 40/2 = 20 s. -
Q10 Medium
A car travels 150 km at 75 km/h and then 150 km at 50 km/h. What is the average speed for the entire journey of 300 km?
ExplanationTotal 300 km in 2 + 3 = 5 h. Average = 60 km/h. -
Q11 Easy
Two cyclists start from points 48 km apart and ride toward each other at 16 km/h and 20 km/h respectively. After how many hours will they meet?
ExplanationTime = 48/36 = 1.33 hours. -
Q12 Hard
A train 200 metres long moving at 90 km/h overtakes another train 100 metres long moving at 54 km/h in the same direction. How many seconds will it take for the first train to completely pass the second?
ExplanationRelative = 36 km/h = 10 m/s. Distance = 300 m. Time = 300/10 = 30 s. -
Q13 Medium
Which of the following journeys has an average speed of 48 km/h for the entire trip?
ExplanationOption A: 240 km in 5 h = 48 km/h average. -
Q14 Easy
A car moving at 60 km/h is 30 km behind another car moving at 45 km/h in the same direction. After how many hours will the first car catch up with the second?
ExplanationRelative = 15 km/h. Time = 30/15 = 2 hours.
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DS1 Easy
A car makes a round trip over the same route. What is the average speed for the entire journey?
Statement IThe car travels 120 km at 60 km/h and returns 120 km at 40 km/h.
Statement IIThe total distance covered is 240 km and the total time taken is 5 hours.
ExplanationEach gives average = 240/5 = 48 km/h. -
DS2 Easy
Two trains start from stations a certain distance apart and move toward each other. After how many hours will they meet?
Statement IThe two trains are 200 km apart when they start.
Statement IIThe trains move toward each other at speeds of 50 km/h and 70 km/h respectively.
ExplanationTime = 200/120 = 1.67 hours.
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DS3 Hard
A boat travels on a river, first downstream and then upstream over the same distance. What is the total time for the journey?
Statement IThe boat can travel at 12 km/h in still water, the stream speed is 3 km/h, and it covers 30 km downstream.
Statement IIThe same boat returns 30 km upstream over the same route.
ExplanationDown 2 h, up 3.33 h. Total ≈ 5.33 hours. -
DS4 Easy
A vehicle completes a journey in two equal parts. Is the average speed for the entire journey 50 km/h?
Statement IThe vehicle covers 100 km at 50 km/h and then another 100 km at 50 km/h.
Statement IIThe total distance covered is 200 km in 4 hours.
ExplanationEach gives average = 50 km/h.