time and motion set #3

Numerical Questions and Solutions

1. A car covers 90 km in 1.5 hours. What is its speed in km/h?
Speed = Distance / Time = 90 km / 1.5 h = 60 km/h.
2. A pendulum completes 30 oscillations in 45 seconds. Calculate its frequency.
Frequency = Number of oscillations / Time = 30 / 45 = 0.67 Hz.
3. Convert 54 km/h to m/s.
Speed = 54 × 1000 / 3600 = 15 m/s.
4. A train moves 200 km in 4 hours. Determine its average speed.
Average speed = Total distance / Total time = 200 km / 4 h = 50 km/h.
5. A cyclist travels 20 km at 10 km/h and then 10 km at 20 km/h. Find the average speed.
Total distance = 20 + 10 = 30 km; Total time = (20 / 10) + (10 / 20) = 2 + 0.5 = 2.5 hours; Average speed = 30 / 2.5 = 12 km/h.
6. A bullet travels 3 km in 2 seconds. Calculate its speed in m/s.
Speed = 3000 m / 2 s = 1500 m/s.
7. A car accelerates uniformly from rest to 72 km/h in 10 seconds. Find the acceleration in m/s².
Acceleration = (Final speed – Initial speed) / Time = (72 × 1000 / 3600) / 10 = 2 m/s².
8. A pendulum completes one oscillation in 1.2 seconds. How many oscillations will it complete in 2 minutes?
Number of oscillations = Total time / Time per oscillation = 120 / 1.2 = 100 oscillations.
9. A car decelerates from 30 m/s to 10 m/s in 5 seconds. What is its deceleration?
Deceleration = (Initial speed – Final speed) / Time = (30 – 10) / 5 = 4 m/s².
10. A cyclist travels at 25 km/h for 36 minutes. Find the distance covered.
Distance = Speed × Time = 25 × (36 / 60) = 15 km.
11. A train moves at 50 km/h for 3 hours and then at 60 km/h for 2 hours. Calculate the total distance covered.
Distance = (50 × 3) + (60 × 2) = 150 + 120 = 270 km.
12. A bus covers 20 km in 40 minutes and another 40 km in 1 hour. Calculate its average speed.
Total distance = 20 + 40 = 60 km; Total time = (40 / 60) + 1 = 1.67 hours; Average speed = 60 / 1.67 ≈ 35.93 km/h.

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