A car moves in a straight line at 24.0 m/s for 10.0 miles, then at 30.0 m/s for another 10.0 miles.
(a) Is the car's average speed less than, greater than, or equal to 27.0 m/s?
less than 27.0 m/s
equal to 27.0 m/s
greater than 27.0 m/s
(b) Calculate the car's average speed. (Enter your answer to three significant figures.)
1 mile = 1609 meters
10 miles = 16090 meters
16090m/(24.0m/s) = 670s
16090m/(30.0m/s) = 536s
Average Speed = Total distance/Elapsed time
Average Speed = [16090m(2)]/(670s+536s) = 32080m/1206s = 26.7m/s
(a) The car's average speed is less than 27.0m/s
(b) The car's average speed is 26.7m/s
One typo: In the average speed calculation, 16090m(2) = 32180m, 32080m. The final answer is still correct.
(a) Well, to figure out if the car's average speed is less than, greater than, or equal to 27.0 m/s, we need to bust out some mad math skills. But since I'm a clown bot and not a math bot, let's take a shortcut. If the car is speeding up from 24.0 m/s to 30.0 m/s, it means the average speed has to be greater than 27.0 m/s. So, the answer is greater than 27.0 m/s.
(b) To calculate the car's average speed, we gotta add up the distances traveled and then divide it by the total time taken. The total distance traveled is 20.0 miles (10.0 miles + 10.0 miles). Now let's convert that to meters because we're fancy like that. 1 mile is equal to about 1609.34 meters, so 20.0 miles is approximately 32,186.8 meters.
The total time taken is the sum of the time taken for each leg of the journey. The first leg, at 24.0 m/s, would take 10.0 miles / 24.0 m/s = approximately 0.4167 hours. The second leg, at 30.0 m/s, would take 10.0 miles / 30.0 m/s = approximately 0.3333 hours.
So the total time taken is 0.4167 hours + 0.3333 hours = approximately 0.75 hours.
Now, to calculate the average speed, we divide the total distance traveled by the total time taken: 32,186.8 meters / 0.75 hours ≈ 42,915.73 meters per hour.
Rounding that to three significant figures, the car's average speed is approximately 42,900 meters per hour.
To find the average speed, we need to calculate the total distance traveled and divide it by the total time taken.
For the first part of the trip, the car traveled at a speed of 24.0 m/s for a distance of 10.0 miles. We need to convert the distance from miles to meters to match the unit of speed. 1 mile is equal to 1609.34 meters.
Distance traveled in the first part of the trip = 10.0 miles * 1609.34 meters/mile = 16093.4 meters
To calculate the time taken for the first part of the trip, we can use the formula:
Time = Distance / Speed
Time taken for the first part of the trip = 16093.4 meters / 24.0 m/s = 670.9 seconds
Similarly, for the second part of the trip, the car traveled at a speed of 30.0 m/s for a distance of 10.0 miles.
Distance traveled in the second part of the trip = 10.0 miles * 1609.34 meters/mile = 16093.4 meters
Time taken for the second part of the trip = 16093.4 meters / 30.0 m/s = 536.5 seconds
Now, to find the total distance and total time, we can add up the values from both parts of the trip:
Total distance = 16093.4 meters + 16093.4 meters = 32,186.8 meters
Total time = 670.9 seconds + 536.5 seconds = 1207.4 seconds
Finally, to find the average speed, we divide the total distance by the total time:
Average speed = Total distance / Total time = 32,186.8 meters / 1207.4 seconds = 26.65 m/s.
Therefore, the car's average speed is less than 27.0 m/s.
To determine the car's average speed, we need to divide the total distance traveled by the total time taken.
Let's start by converting the distances given into meters:
10.0 miles x 1609.34 meters/mile = 16,093.4 meters
Now let's calculate the total time taken:
For the first part of the journey: distance = 16,093.4 meters, speed = 24.0 m/s
Time taken = distance / speed = 16,093.4 m / 24.0 m/s = 670.5583 seconds
For the second part of the journey: distance = 16,093.4 meters, speed = 30.0 m/s
Time taken = distance / speed = 16,093.4 m / 30.0 m/s = 536.4478 seconds
Now, let's calculate the total time for the entire journey:
Total time = time taken for the first part + time taken for the second part
Total time = 670.5583 s + 536.4478 s = 1207.0061 seconds
Next, let's calculate the average speed:
Average speed = total distance / total time
Average speed = (2 x 16,093.4 m) / 1207.0061 s = 26.659 m/s
So, the car's average speed is 26.659 m/s.
(a) The car's average speed is less than 27.0 m/s.
(b) The car's average speed is 26.659 m/s.