Numerical Questions and Solutions
1. A car travels 45 km at a speed of 60 km/h. How much time will it take to complete the journey?
Time = Distance / Speed = 45 km / 60 km/h = 0.75 hours or 45 minutes.
2. Reema observes her pendulum completes 20 oscillations in 40 seconds. What is its frequency?
Frequency = Number of oscillations / Time = 20 / 40 = 0.5 Hz.
3. A train moves 150 km in 3 hours. What is its average speed?
Average speed = Total distance / Total time = 150 km / 3 h = 50 km/h.
4. A bus covers a distance of 24 km in 30 minutes. Find its speed in km/h.
Speed = Distance / Time = 24 / (30 / 60) = 48 km/h.
5. Convert 90 km/h to m/s.
Speed = 90 × 1000 / 3600 = 25 m/s.
6. A pendulum completes 50 oscillations in 100 seconds. Calculate its time period.
Time period = Total time / Number of oscillations = 100 / 50 = 2 seconds.
7. A cyclist covers 12 km in 40 minutes. Calculate his speed in km/h.
Speed = Distance / Time = 12 / (40 / 60) = 18 km/h.
8. A bus starts from rest and covers the following distances at regular intervals: 0 m (0 s), 8 m (2 s), 16 m (4 s), 24 m (6 s), 32 m (8 s). What can you conclude about the motion of the bus?
The bus has uniform motion as it covers equal distances in equal intervals of time.
9. A car travels 20 km in 20 minutes and then 40 km in 40 minutes. Find its average speed.
Total distance = 20 + 40 = 60 km; Total time = 20/60 + 40/60 = 1 hour; Average speed = 60 km/h.
10. A clock’s pendulum completes one oscillation in 1.5 seconds. How many oscillations will it complete in 3 minutes?
Number of oscillations = Total time / Time per oscillation = 180 / 1.5 = 120 oscillations.
11. A car moves at a constant speed of 50 km/h for 2 hours and then at 70 km/h for 3 hours. Calculate the total distance covered.
Distance = (50 × 2) + (70 × 3) = 100 + 210 = 310 km.
12. A pendulum completes 30 oscillations in 60 seconds. Calculate its frequency and time period.
Frequency = Number of oscillations / Time = 30 / 60 = 0.5 Hz;
Time period = 1 / Frequency = 1 / 0.5 = 2 seconds.
Time period = 1 / Frequency = 1 / 0.5 = 2 seconds.