Answer :
Sure! Let's break down each part of the question and understand the calculations step by step.
Part A: Average Speed on a 2000m Sprint
1. Distance Covered: 2000 meters.
2. Time Taken: 6 minutes and 30 seconds.
- Convert the time into seconds: [tex]\(6 \times 60 + 30 = 390\)[/tex] seconds.
3. Average Speed Calculation:
- Average speed is calculated by dividing the total distance by the total time taken.
- Average speed = [tex]\(\text{Distance} / \text{Time} = 2000 / 390\)[/tex].
4. Result: The average speed for the 2000m sprint is approximately 5.13 meters per second (m/s).
Part B: Acceleration and Final Speed for a 500m Sprint
1. Distance Covered: 500 meters.
2. Time Taken: 1 minute and 20 seconds.
- Convert the time into seconds: [tex]\(1 \times 60 + 20 = 80\)[/tex] seconds.
3. Acceleration Calculation:
- It is assumed that the sprint starts from rest and the acceleration is constant.
- Use the formula for constant acceleration: [tex]\( \text{Distance} = \frac{1}{2} \times \text{Acceleration} \times (\text{Time})^2 \)[/tex].
- Rearranging to find acceleration: [tex]\(\text{Acceleration} = 2 \times \text{Distance} / (\text{Time})^2 = 2 \times 500 / (80)^2\)[/tex].
- This calculates to an acceleration of approximately 0.15625 meters per second squared (m/s²).
4. Final Speed Calculation at 500m:
- The final speed at the end of the distance is given by: [tex]\(\text{Final speed} = \text{Acceleration} \times \text{Time} = 0.15625 \times 80\)[/tex].
- The final speed is 12.5 meters per second (m/s).
Part C: Course Length for Boat C
1. Average Speed during the Course: 7.8 meters per second.
2. Time Taken: 32 minutes and 4 seconds.
- Convert the time into seconds: [tex]\(32 \times 60 + 4 = 1924\)[/tex] seconds.
3. Course Length Calculation:
- The course length is calculated by multiplying the average speed by the total time taken.
- Course length = [tex]\(\text{Average speed} \times \text{Time} = 7.8 \times 1924\)[/tex].
4. Result: The length of the course is approximately 15,007.2 meters.
These are the solutions to the given problem parts, calculated based on the data provided.
Part A: Average Speed on a 2000m Sprint
1. Distance Covered: 2000 meters.
2. Time Taken: 6 minutes and 30 seconds.
- Convert the time into seconds: [tex]\(6 \times 60 + 30 = 390\)[/tex] seconds.
3. Average Speed Calculation:
- Average speed is calculated by dividing the total distance by the total time taken.
- Average speed = [tex]\(\text{Distance} / \text{Time} = 2000 / 390\)[/tex].
4. Result: The average speed for the 2000m sprint is approximately 5.13 meters per second (m/s).
Part B: Acceleration and Final Speed for a 500m Sprint
1. Distance Covered: 500 meters.
2. Time Taken: 1 minute and 20 seconds.
- Convert the time into seconds: [tex]\(1 \times 60 + 20 = 80\)[/tex] seconds.
3. Acceleration Calculation:
- It is assumed that the sprint starts from rest and the acceleration is constant.
- Use the formula for constant acceleration: [tex]\( \text{Distance} = \frac{1}{2} \times \text{Acceleration} \times (\text{Time})^2 \)[/tex].
- Rearranging to find acceleration: [tex]\(\text{Acceleration} = 2 \times \text{Distance} / (\text{Time})^2 = 2 \times 500 / (80)^2\)[/tex].
- This calculates to an acceleration of approximately 0.15625 meters per second squared (m/s²).
4. Final Speed Calculation at 500m:
- The final speed at the end of the distance is given by: [tex]\(\text{Final speed} = \text{Acceleration} \times \text{Time} = 0.15625 \times 80\)[/tex].
- The final speed is 12.5 meters per second (m/s).
Part C: Course Length for Boat C
1. Average Speed during the Course: 7.8 meters per second.
2. Time Taken: 32 minutes and 4 seconds.
- Convert the time into seconds: [tex]\(32 \times 60 + 4 = 1924\)[/tex] seconds.
3. Course Length Calculation:
- The course length is calculated by multiplying the average speed by the total time taken.
- Course length = [tex]\(\text{Average speed} \times \text{Time} = 7.8 \times 1924\)[/tex].
4. Result: The length of the course is approximately 15,007.2 meters.
These are the solutions to the given problem parts, calculated based on the data provided.
