Final answer:
In the first question, the athlete's final speed is calculated using the formula: Final speed = Initial speed + (Acceleration x Time). In the second question, the cyclist's average speed is calculated by dividing the change in speed by the time interval. In the third question, the distance moved by the car during acceleration is calculated using the formula: Distance = (Initial speed x Time) + (0.5 x Acceleration x (Time^2)).
Step-by-step explanation:
In the first question, the athlete accelerates from rest at a constant rate of 3.0 m/s² for 4s. To calculate the final speed of the athlete, we can use the formula:
Final speed = Initial speed + (Acceleration x Time)
Plugging in the values:
Final speed = 0 + (3.0 m/s² x 4s) = 12 m/s
So, the final speed of the athlete is 12 m/s.
In the second question, the cyclist increases his speed from 10 m/s to 20 m/s in 5s. To calculate the average speed over this time interval, we can use the formula:
Average speed = Total distance traveled / Total time
Here, the total distance traveled is the change in speed times the time interval, so:
Average speed = (20 m/s - 10 m/s) / 5s = 2 m/s
Therefore, the average speed of the cyclist over this time interval is 2 m/s.
In the third question, the car accelerates from rest at a constant rate of 2 m/s² for 5s. To calculate the distance moved by the car, we can use the formula:
Distance = (Initial speed x Time) + (0.5 x Acceleration x (Time^2))
Since the car starts from rest, the initial speed is 0 m/s, so the formula simplifies to:
Distance = 0 + (0.5 x 2 m/s² x (5s)^2) = 25 m
The car moves a distance of 25 meters during this acceleration.
Learn more about Calculating final speed, average speed, and distance during acceleration