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 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 at 2:00 PM and covers the following distances: 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 be drawn about the motion of the bus?
The motion of the bus is uniform since equal distances are covered in equal intervals of time.
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 covers 6 km in 40 minutes, stops for 5 minutes, and completes her 3 km journey in 15 minutes. What is her average speed?
Total distance = 9 km, Total time = 40 + 5 + 15 = 60 minutes or 1 hour. Average speed = Total distance / Total time = 9 km/h.
8. Convert a speed of 0.06 m/s to km/h.
Speed = 0.06 × 3600 / 1000 = 0.216 km/h.
9. A car is running at a uniform speed. Its distance-time graph is a straight line. What conclusion can be drawn about its motion?
The motion is uniform since the graph indicates constant speed.
10. A car moves with a speed of 30 km/h for 10 minutes. Calculate the distance covered.
Distance = Speed × Time = 30 × (10/60) = 5 km.
11. A train moves 120 km in 2 hours and then 60 km in 1 hour. What is its average speed?
Total distance = 120 + 60 = 180 km, Total time = 2 + 1 = 3 hours. Average speed = 180 / 3 = 60 km/h.
12. If a sundial is used for time measurement, what is the accuracy affected by?
The accuracy of a sundial is affected by the sun’s position, weather conditions, and the sundial’s alignment.