Shortcut Methods and Tricks to Solve Numericals on the topic of Frame of Reference- Motion in a Straight Line- Uniform:

1. To convert km/h to m/s, multiply the speed in km/h by 5/18.
2. To convert m/s to km/h, multiply the speed in m/s by 18/5.
3. To convert km/h to mph, multiply the speed in km/h by 0.621371.
4. To convert mph to km/h, multiply the speed in mph by 1.60934.
5. To convert knots to km/h, multiply the speed in knots by 1.852.
6. To convert km/h to knots, multiply the speed in km/h by 0.539957.
7. To calculate the distance traveled by an object in a given time, use the formula: distance = speed × time.
8. To calculate the speed of an object, use the formula: speed = distance traveled ÷ time taken.
9. To calculate the time taken by an object to travel a given distance, use the formula: time taken = distance traveled ÷ speed.

Examples:

1. A car is moving with a speed of 60 km/h. What is the speed of the car in m/s? Solution: Speed in m/s = 60 km/h × 5/18 = 50/3 m/s ≈ 16.67 m/s

2. A train is moving with a speed of 90 km/h. What is the speed of the train in miles per hour (mph)? Solution: Speed in mph = 90 km/h × 0.621371 = 55.9234 mph ≈ 56 mph

3. A plane is flying at a speed of 500 km/h. What is the speed of the plane in knots? Solution: Speed in knots = 500 km/h × 0.539957 = 270 knots

4. A boat is moving with a speed of 10 knots. What is the speed of the boat in km/h? Solution: Speed in km/h = 10 knots × 1.852 = 18.52 km/h ≈ 19 km/h

5. A cyclist is riding at a speed of 15 mph. What is the speed of the cyclist in m/s? Solution: Speed in m/s = 15 mph × 1609.34/3600 ≈ 4.17 m/s

6. A runner is running at a speed of 10 m/s. What is the speed of the runner in km/h? Solution: Speed in km/h = 10 m/s × 3600/1000 = 36 km/h

7. A person is walking at a speed of 5 km/h. What is the speed of the person in m/s? Solution: Speed in m/s = 5 km/h × 1000/3600 = 1.389 m/s

8. A car is moving with a speed of 60 km/h. What is the distance traveled by the car in 5 seconds? Solution: Distance traveled = Speed × Time = 60 km/h × 5/3600 = 0.833 km

9. A train is moving with a speed of 90 km/h. What is the distance traveled by the train in 10 minutes? Solution: First, convert the time to hours: 10 minutes = 10/60 = 1/6 hours. Distance traveled = Speed × Time = 90 km/h × 1/6 = 15 km

10. A plane is flying at a speed of 500 km/h. What is the distance traveled by the plane in 1 hour? Solution: Distance traveled = Speed × Time = 500 km/h × 1 = 500 km