Step-by-step explanation:
1. To calculate the distance covered by the roller coaster in 5.5 seconds, we can use the formula:
Distance = Speed × Time
Given:
Speed = 12 m/s
Time = 5.5 s
Plugging in the values, we get:
Distance = 12 m/s × 5.5 s = 66 meters
Therefore, the roller coaster covers a distance of 66 meters in 5.5 seconds.
2. To determine the time it takes for the ball to cover a distance of 0.23 meters, we can use the formula:
Time = Distance / Speed
Given:
Distance = 0.23 m
Speed = 0.76 m/s
Plugging in the values, we get:
Time = 0.23 m / 0.76 m/s = 0.3026 seconds (rounded to four decimal places)
Therefore, it takes approximately 0.3026 seconds for the ball to cover a distance of 0.23 meters.
3. The velocity of an object is calculated by dividing the change in position by the time taken. In this case, the object moves from 73 m to 62 m in 12 seconds. The formula for velocity is:
Velocity = (Final Position - Initial Position) / Time
Given:
Initial Position = 73 m
Final Position = 62 m
Time = 12 s
Plugging in the values, we get:
Velocity = (62 m - 73 m) / 12 s = -0.92 m/s
Therefore, the velocity of the object is -0.92 m/s. The negative sign indicates that the object is moving in the opposite direction to the positive axis.
4. To calculate the total distance traveled by the comet, we need to multiply its speed by the time traveled. The comet is traveling at a speed of 50,000 km/hr for 4 hours. We need to convert the speed to meters per second and the time to seconds for consistent units.
Given:
Speed = 50,000 km/hr = 50,000,000 m/3600 s ≈ 13,889 m/s
Time = 4 hours = 4 × 3600 s = 14,400 s
Plugging in the values, we get:
Distance = Speed × Time = 13,889 m/s × 14,400 s ≈ 200,000,000 meters
Therefore, the comet travels approximately 200,000,000 meters in 4 hours.
5. To calculate the average speed over the entire 2.4-minute interval, we need to find the total distance traveled and divide it by the total time taken.
Given:
First phase: Tortoise speed = 0.060 m/s, Time = 1.2 minutes = 1.2 × 60 s = 72 seconds
Second phase: Finch’s flight speed = 13 m/s, Time = 1.2 minutes = 1.2 × 60 s = 72 seconds
Total Time = 72 s + 72 s = 144 s
Total Distance = Distance traveled during the tortoise phase + Distance traveled during the flight phase
= (0.060 m/s × 72 s) + (13 m/s × 72 s)
= 4.32 m + 936 m
= 940.32 m
Average Speed = Total Distance / Total Time = 940.32 m / 144 s ≈ 6.53 m/s (rounded to two decimal places)
Therefore, the average speed of the finch over the entire 2.4-minute interval is approximately 6.53 m/s.