Here are the step-by-step solutions for each problem on your worksheet.
1. Convert 144 km/hr to m/sec
*
Step 1: To change kilometers per hour (km/hr) to meters per second (m/sec), you multiply by $\frac{5}{18}$.
*
Step 2: Calculation: $144 \times \frac{5}{18}$
*
Step 3: First, divide 144 by 18, which equals 8. Then multiply 8 by 5.
*
Step 4: $8 \times 5 = 40$.
2. Convert 30 m/sec to km/hr
*
Step 1: To change meters per second (m/sec) to kilometers per hour (km/hr), you multiply by $\frac{18}{5}$.
*
Step 2: Calculation: $30 \times \frac{18}{5}$
*
Step 3: First, divide 30 by 5, which equals 6. Then multiply 6 by 18.
*
Step 4: $6 \times 18 = 108$.
3. Train passing a platform
*
Step 1: When a train passes a platform, it must cover its own length plus the length of the platform.
* Total Distance = Length of Train + Length of Platform
* Total Distance = $130 \text{ m} + 270 \text{ m} = 400 \text{ meters}$.
*
Step 2: Use the formula: $\text{Time} = \frac{\text{Distance}}{\text{Speed}}$.
*
Step 3: The speed is given as 40 meters per second.
*
Step 4: Calculation: $\frac{400}{40} = 10$.
4. Raina's car distance
*
Step 1: First, convert the time into hours so it matches the speed unit (km/h).
* 30 minutes is half an hour ($0.5$ hours).
* Total Time = $2 \text{ hours} + 0.5 \text{ hours} = 2.5 \text{ hours}$.
*
Step 2: Use the formula: $\text{Distance} = \text{Speed} \times \text{Time}$.
*
Step 3: Calculation: $50 \times 2.5$.
*
Step 4: $50 \times 2 = 100$ and $50 \times 0.5 = 25$. Add them together: $100 + 25 = 125$.
5. Mr. Manav's walking distance
*
Step 1: The speed is in meters per second (m/s), but the time is in minutes. We need to convert the time to seconds.
* 1 minute = 60 seconds.
* Total Time = $40 \times 60 = 2400 \text{ seconds}$.
*
Step 2: Use the formula: $\text{Distance} = \text{Speed} \times \text{Time}$.
*
Step 3: Calculation: $1.5 \times 2400$.
*
Step 4: An easy way to do this is to think of $1.5$ as $1 + 0.5$.
* $1 \times 2400 = 2400$
* $0.5 \times 2400 = 1200$ (half of 2400)
* $2400 + 1200 = 3600 \text{ meters}$.
6. Train speed in km/hr
*
Step 1: The distance is already in kilometers (500 km), but the time is in minutes (600 min). We need to convert the time to hours.
* There are 60 minutes in 1 hour.
* Time in hours = $\frac{600}{60} = 10 \text{ hours}$.
*
Step 2: Use the formula: $\text{Speed} = \frac{\text{Distance}}{\text{Time}}$.
*
Step 3: Calculation: $\frac{500}{10} = 50$.
──────────────────────────────────────
Final Answer:
1. 40 m/sec
2. 108 km/hr
3. 10 seconds
4. 125 km
5. 3600 meters
6. 50 km/hr
Parent Tip: Review the logic above to help your child master the concept of speed distance and time worksheet.
