Numerical Questions and Solutions
1. A car is running at a speed of 60 km/h. How much time will it take to cover a distance of 27 km?
Time = Distance / Speed = 27 km / 60 km/h = 0.45 hours or 27 minutes.
2. Reema observes her wall clock’s pendulum completes 15 oscillations in 30 seconds. What is the time period of the pendulum?
Time period = Total time / Number of oscillations = 30 s / 15 = 2 seconds.
3. A bus starts from rest and covers the following distances at regular intervals: 0 m (0 s), 5 m (2 s), 10 m (4 s), 15 m (6 s), 20 m (8 s), and 25 m (10 s). What conclusion can you draw about the motion of the bus?
The motion of the bus is uniform since equal distances are covered in equal time intervals.
4. A car moves at 40 km/h for 15 minutes and 60 km/h for the next 15 minutes. What is the total distance covered?
Distance = (Speed₁ × Time₁) + (Speed₂ × Time₂) = (40 × 0.25) + (60 × 0.25) = 10 + 15 = 25 km.
5. Calculate the frequency if a pendulum completes 40 oscillations in 60 seconds.
Frequency = Number of oscillations / Time = 40 / 60 = 0.67 Hz.
6. Determine the time period of a pendulum with a frequency of 0.67 Hz.
Time period = 1 / Frequency = 1 / 0.67 = 1.5 seconds.
7. Sonia cycles 6 km in 40 minutes, stops for 5 minutes, and then completes the remaining 3 km in 15 minutes. What is her average speed for the journey?
Total distance = 9 km; Total time = 40 + 5 + 15 = 60 minutes or 1 hour. Average speed = Total distance / Total time = 9 km/h.
8. A speed of 0.06 m/s is given. Convert this speed into km/h.
Speed = 0.06 × 3600 / 1000 = 0.216 km/h.
9. A car covers a distance of 10 km in 10 minutes. Find its speed in km/h.
Speed = Distance / Time = 10 km / (10/60 h) = 60 km/h.
10. A train moves 240 km in 4 hours. What is its average speed?
Average speed = Total distance / Total time = 240 km / 4 h = 60 km/h.
11. A pendulum takes 2 seconds to complete one oscillation. How many oscillations will it complete in 1 minute?
Number of oscillations = Total time / Time per oscillation = 60 / 2 = 30 oscillations.
12. A car travels at a speed of 50 km/h for 3 hours. Calculate the total distance covered.
Distance = Speed × Time = 50 km/h × 3 h = 150 km.