Time and Motion Problems
1. A car travels at a speed of 60 km/h for 3 hours. Calculate the distance covered.
Distance = Speed × Time
[ text{Distance} = 60 , text{km/h} times 3 , text{hours} = 180 , text{km} ]
2. A cyclist covers 20 km in 40 minutes. Find his speed in km/h.
Speed = Distance / Time
[ text{Time} = frac{40 , text{minutes}}{60} = 0.666 , text{hours} ]
[ text{Speed} = frac{20 , text{km}}{0.666 , text{hours}} approx 30 , text{km/h} ]
3. A train moves at 90 km/h for 2 hours. Calculate the distance covered.
Distance = Speed × Time
[ text{Distance} = 90 , text{km/h} times 2 , text{hours} = 180 , text{km} ]
4. Convert a speed of 45 km/h to m/s.
Speed in m/s = Speed in km/h × (1000 m / 1 km) × (1 hour / 3600 seconds)
[ text{Speed} = 45 times frac{1000}{3600} = 12.5 , text{m/s} ]
5. A pendulum completes 50 oscillations in 25 seconds. Calculate its frequency.
Frequency = Number of oscillations / Time
[ text{Frequency} = frac{50}{25 , text{seconds}} = 2 , text{Hz} ]
6. A car moves at 70 km/h for 1.5 hours. Calculate the distance covered.
Distance = Speed × Time
[ text{Distance} = 70 , text{km/h} times 1.5 , text{hours} = 105 , text{km} ]
7. A bus covers 120 km in 2.5 hours. Calculate its speed in km/h.
Speed = Distance / Time
[ text{Speed} = frac{120 , text{km}}{2.5 , text{hours}} = 48 , text{km/h} ]
8. Convert a speed of 20 m/s to km/h.
Speed in km/h = Speed in m/s × (3600 seconds / 1 hour) × (1 km / 1000 m)
[ text{Speed} = 20 times frac{3600}{1000} = 72 , text{km/h} ]
9. A cyclist covers 30 km in 1 hour 30 minutes. What is his speed in km/h?
Speed = Distance / Time
[ text{Time} = 1 , text{hour} + frac{30 , text{minutes}}{60} = 1.5 , text{hours} ]
[ text{Speed} = frac{30 , text{km}}{1.5 , text{hours}} = 20 , text{km/h} ]
10. A pendulum’s frequency is 0.25 Hz. Calculate its time period.
Time period = 1 / Frequency
[ text{Time period} = frac{1}{0.25} = 4 , text{seconds} ]
11. A car moves at 25 m/s for 4 minutes. Calculate the distance covered in kilometers.
Distance in meters = Speed × Time
[ text{Time} = 4 , text{minutes} times 60 = 240 , text{seconds} ]
[ text{Distance} = 25 , text{m/s} times 240 = 6000 , text{meters} ]
[ text{Distance in kilometers} = frac{6000}{1000} = 6 , text{km} ]
12. A train moves at 120 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} = 120 , text{km/h} times 0.75 , text{hours} = 90 , text{km} ]