Time and Motion Problems – Set 2
1. A car moves at a speed of 80 km/h for 4 hours. Calculate the distance covered.
Distance = Speed × Time
\[ \text{Distance} = 80 \, \text{km/h} \times 4 \, \text{hours} = 320 \, \text{km} \]
2. A cyclist travels 18 km in 45 minutes. Find his speed in km/h.
Speed = Distance / Time
\[ \text{Time} = \frac{45 \, \text{minutes}}{60} = 0.75 \, \text{hours} \]
\[ \text{Speed} = \frac{18 \, \text{km}}{0.75 \, \text{hours}} = 24 \, \text{km/h} \]
3. Convert a speed of 50 km/h to m/s.
Speed in m/s = Speed in km/h × (1000 m / 1 km) × (1 hour / 3600 seconds)
\[ \text{Speed} = 50 \times \frac{1000}{3600} \approx 13.89 \, \text{m/s} \]
4. A train travels 180 km at a speed of 90 km/h. How long does the journey take?
Time = Distance / Speed
\[ \text{Time} = \frac{180 \, \text{km}}{90 \, \text{km/h}} = 2 \, \text{hours} \]
5. A pendulum completes 90 oscillations in 30 seconds. Calculate its frequency.
Frequency = Number of oscillations / Time
\[ \text{Frequency} = \frac{90}{30 \, \text{seconds}} = 3 \, \text{Hz} \]
6. A bus travels at 60 km/h for 2.5 hours. Calculate the distance covered.
Distance = Speed × Time
\[ \text{Distance} = 60 \, \text{km/h} \times 2.5 \, \text{hours} = 150 \, \text{km} \]
7. Convert a speed of 25 m/s to km/h.
Speed in km/h = Speed in m/s × (3600 seconds / 1 hour) × (1 km / 1000 m)
\[ \text{Speed} = 25 \times \frac{3600}{1000} = 90 \, \text{km/h} \]
8. A car travels 90 km in 1.5 hours. Find its speed in km/h.
Speed = Distance / Time
\[ \text{Speed} = \frac{90 \, \text{km}}{1.5 \, \text{hours}} = 60 \, \text{km/h} \]
9. A train travels at 110 km/h for 3.5 hours. Calculate the distance covered.
Distance = Speed × Time
\[ \text{Distance} = 110 \, \text{km/h} \times 3.5 \, \text{hours} = 385 \, \text{km} \]
10. A pendulum’s frequency is 0.5 Hz. What is its time period?
Time period = 1 / Frequency
\[ \text{Time period} = \frac{1}{0.5} = 2 \, \text{seconds} \]
11. A cyclist takes 2 hours to travel 60 km. What is his average speed?
Average Speed = Distance / Time
\[ \text{Average Speed} = \frac{60 \, \text{km}}{2 \, \text{hours}} = 30 \, \text{km/h} \]
12. A car moves at 15 m/s for 10 minutes. Calculate the distance covered in kilometers.
Distance in meters = Speed × Time
\[ \text{Time} = 10 \, \text{minutes} \times 60 = 600 \, \text{seconds} \]
\[ \text{Distance} = 15 \, \text{m/s} \times 600 = 9000 \, \text{meters} \]
\[ \text{Distance in kilometers} = \frac{9000}{1000} = 9 \, \text{km} \]