Time and Motion Problems – Set 3
1. A bus travels 150 km in 2 hours 30 minutes. Calculate its speed in km/h.
Speed = Distance / Time
[ text{Time} = 2 , text{hours} + frac{30 , text{minutes}}{60} = 2.5 , text{hours} ]
[ text{Speed} = frac{150 , text{km}}{2.5 , text{hours}} = 60 , text{km/h} ]
2. Convert a speed of 90 km/h to m/s.
Speed in m/s = Speed in km/h × (1000 m / 1 km) × (1 hour / 3600 seconds)
[ text{Speed} = 90 times frac{1000}{3600} = 25 , text{m/s} ]
3. A car covers 240 km in 4 hours. What is its average speed?
Average Speed = Distance / Time
[ text{Average Speed} = frac{240 , text{km}}{4 , text{hours}} = 60 , text{km/h} ]
4. A cyclist rides at a speed of 12 km/h for 45 minutes. Calculate the distance covered.
Distance = Speed × Time
[ text{Time} = frac{45 , text{minutes}}{60} = 0.75 , text{hours} ]
[ text{Distance} = 12 , text{km/h} times 0.75 , text{hours} = 9 , text{km} ]
5. A train travels at a constant speed of 100 km/h for 3 hours and 15 minutes. Find the total distance covered.
Distance = Speed × Time
[ text{Time} = 3 , text{hours} + frac{15 , text{minutes}}{60} = 3.25 , text{hours} ]
[ text{Distance} = 100 , text{km/h} times 3.25 , text{hours} = 325 , text{km} ]
6. A car moves at 72 km/h. How long will it take to cover 180 km?
Time = Distance / Speed
[ text{Time} = frac{180 , text{km}}{72 , text{km/h}} = 2.5 , text{hours} ]
7. A bus travels 30 km at 40 km/h and then 50 km at 60 km/h. Calculate the total travel time.
Time = Distance / Speed
[ text{Time for first part} = frac{30 , text{km}}{40 , text{km/h}} = 0.75 , text{hours} ]
[ text{Time for second part} = frac{50 , text{km}}{60 , text{km/h}} approx 0.833 , text{hours} ]
[ text{Total time} = 0.75 + 0.833 approx 1.583 , text{hours} ]
8. Convert a speed of 5 m/s to km/h.
Speed in km/h = Speed in m/s × (3600 seconds / 1 hour) × (1 km / 1000 m)
[ text{Speed} = 5 times frac{3600}{1000} = 18 , text{km/h} ]
9. A pendulum completes 200 oscillations in 1 minute. Find its frequency.
Frequency = Number of oscillations / Time
[ text{Time} = 1 , text{minute} times 60 = 60 , text{seconds} ]
[ text{Frequency} = frac{200}{60} approx 3.33 , text{Hz} ]
10. A car accelerates uniformly from rest to 20 m/s in 10 seconds. What is the acceleration?
Acceleration = Change in velocity / Time
[ text{Acceleration} = frac{20 , text{m/s} – 0 , text{m/s}}{10 , text{seconds}} = 2 , text{m/s}^2 ]
11. A cyclist travels at 15 km/h for 20 minutes. Calculate the distance covered.
Distance = Speed × Time
[ text{Time} = frac{20 , text{minutes}}{60} = 0.333 , text{hours} ]
[ text{Distance} = 15 , text{km/h} times 0.333 , text{hours} approx 5 , text{km} ]
12. A car moves at 80 km/h for 3 hours and then 60 km/h for 2 hours. Find the total distance covered.
Distance = Speed × Time
[ text{Distance for first part} = 80 , text{km/h} times 3 , text{hours} = 240 , text{km} ]
[ text{Distance for second part} = 60 , text{km/h} times 2 , text{hours} = 120 , text{km} ]
[ text{Total distance} = 240 + 120 = 360 , text{km} ]