1. Convert the given speeds into km/hr. (i) 90 km/hr is already in km/hr. (ii) 27 km/hr is already in km/hr. 2. Convert speeds from m/sec to km/hr using the formula: $$\text{Speed in km/hr} = \text{Speed in m/sec} \times 3.6$$ (i) $35 \times 3.6 = 126$ km/hr (ii) $14 \times 3.6 = 50.4$ km/hr (iii) $60 \times 3.6 = 216$ km/hr (iv) $3.5 \times 3.6 = 12.6$ km/hr 3. Speed of car = $\frac{\text{Distance}}{\text{Time}}$ Time = 3 hours 35 minutes = $3 + \frac{35}{60} = 3.5833$ hours Speed = $\frac{258}{3.5833} \approx 72$ km/hr 4. Speed of train = $\frac{14 \text{ km}}{\frac{8}{60} \text{ hr}} = \frac{14}{0.1333} = 105$ km/hr 5. Speed = $\frac{8}{1 + \frac{15}{60}} = \frac{8}{1.25} = 6.4$ km/hr 6. Distance = Speed $\times$ Time Time = 36 minutes = $\frac{36}{60} = 0.6$ hours Distance = $12 \times 0.6 = 7.2$ km 7. Time = $\frac{\text{Distance}}{\text{Speed}}$ Distance = 600 m = 0.6 km Speed = 4 km/hr Time = $\frac{0.6}{4} = 0.15$ hours = $0.15 \times 60 = 9$ minutes 8. Distance = Speed $\times$ Time Speed = 45 km/hr = $\frac{45}{3600} = 0.0125$ km/sec Time = 8 sec Distance = $0.0125 \times 8 = 0.1$ km = 100 m 9. Convert 10.5 m/sec to km/hr: $10.5 \times 3.6 = 37.8$ km/hr Compare 36 km/hr and 37.8 km/hr: 37.8 km/hr is more. 10. Distance = Speed $\times$ Time = $45 \times 6 = 270$ km New speed = $\frac{270}{5} = 54$ km/hr 11. Distance = Speed $\times$ Time = $45 \times \frac{50}{60} = 37.5$ km Time at 30 km/hr = $\frac{37.5}{30} = 1.25$ hours = 75 minutes 12. Total distance = $100 + 64 + 72 = 236$ km Total time = $2 + 1 + 2 = 5$ hours Average speed = $\frac{236}{5} = 47.2$ km/hr 13. Total distance = $2500 + 1200 + 500 = 4200$ km Time for each segment: $\frac{2500}{500} = 5$ hr, $\frac{1200}{400} = 3$ hr, $\frac{500}{250} = 2$ hr Total time = $5 + 3 + 2 = 10$ hr Average speed = $\frac{4200}{10} = 420$ km/hr 14. Total distance = $36 \times 5 + 45 \times 4 = 180 + 180 = 360$ km Total time = $5 + 4 = 9$ hr Average speed = $\frac{360}{9} = 40$ km/hr 15. Total distance = $4 + 4 = 8$ km Total time = $2.5$ hr Average speed = $\frac{8}{2.5} = 3.2$ km/hr 16. Speed = 60 km/hr = $\frac{60 \times 1000}{3600} = 16.67$ m/sec Length of train = 150 m Time = $\frac{150}{16.67} = 9$ sec 17. Speed = 63 km/hr = $\frac{63 \times 1000}{3600} = 17.5$ m/sec Length = 175 m Time = $\frac{175}{17.5} = 10$ sec 18. Length = 150 m, Time = 6 sec Speed = $\frac{150}{6} = 25$ m/sec = $25 \times 3.6 = 90$ km/hr 19. Length of train = 120 m, Length of bridge = 180 m Total distance = 300 m Speed = 54 km/hr = $\frac{54 \times 1000}{3600} = 15$ m/sec Time = $\frac{300}{15} = 20$ sec 20. Total length = $760 + 440 = 1200$ m Time = 40 sec Speed = $\frac{1200}{40} = 30$ m/sec = $30 \times 3.6 = 108$ km/hr