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murshid_islam
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If we travel s_{1} distance in t_{1} time and s_{2} distance in t_{2} time, is the average speed [tex]\frac{s_1 + s_2}{t_1 + t_2}[/tex] or [tex]\frac{\frac{s_1}{t_1} + \frac{s_2}{t_2}}{2}[/tex]
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Is there any reason why it isn't the second one or is it just defined that way?Doc Al said:The first one: (total distance)/(total time).
I'm sorry, I still don't get it. Why does the second formula, i.e., [tex]\frac{\frac{s_1}{t_1} + \frac{s_2}{t_2}}{2}[/tex] or [tex]\frac{v_1 + v_2}{2}[/tex] not work here? If we use that formula, we get the velocity required downhill to be 90 mph. On the other hand, if I use the first formula, i.e., [tex]\frac{s_1 + s_2}{t_1 + t_2}[/tex], we have,Mark44 said:Here's an old problem that shows why the "average of averages" (as in your second formula) doesn't work.
On a certain road there is a hill that the road goes up and then down the other side. The uphill side is one mile and the downhill side is one mile. If I drive up the hill at an average speed of 30 mph, how fast do I need to drive down the other side to average 60 mph for the two miles?
But why exactly doesn't the second formula, i.e., [tex]\frac{v_1 + v_2}{2}[/tex] work here?Doc Al said:I believe Mark44 made an error in his problem statement. To average 60 mph, you'd have to complete the entire 2 mile trip in 2 minutes. But if you traveled the first half at 30 mph you've already used up 2 minutes. You'd have to travel the second mile in 0 time! (Infinite speed!) Which is impossible, of course.
But the formula works just fine--it tells you that you need to cover that second mile in 0 time.
Well, that formula gives the average of two speeds but it's not the average speed.murshid_islam said:But why exactly doesn't the second formula, i.e., [tex]\frac{v_1 + v_2}{2}[/tex] work here?
But 90 mph isn't the right answer. If the second mile is traveled at a speed of 90 mph, the time it takes would be 1/90 hour. That would make the total time equal to:murshid_islam said:I'm sorry, I still don't get it. Why does the second formula, i.e., [tex]\frac{\frac{s_1}{t_1} + \frac{s_2}{t_2}}{2}[/tex] or [tex]\frac{v_1 + v_2}{2}[/tex] not work here? If we use that formula, we get the velocity required downhill to be 90 mph.
Average speed is the total distance traveled divided by the total time taken to travel that distance. It is a measure of how fast an object is moving on average.
Average speed is calculated by dividing the total distance traveled by the total time taken to travel that distance. The formula for average speed is: average speed = total distance / total time.
Yes, average speed can be negative if an object is traveling in the opposite direction of its initial motion. For example, if a car travels north for 10 miles and then turns around and travels south for 10 miles, its average speed would be 0 miles per hour. However, if the car traveled north for 10 miles and then south for 20 miles, its average speed would be negative 10 miles per hour.
Average speed is the total distance traveled divided by the total time taken, while instantaneous speed is the speed at a specific moment in time. Average speed gives an overall picture of how fast an object is moving, while instantaneous speed can vary based on the object's acceleration or deceleration at any given moment.
Average speed can be affected by various factors such as the distance traveled, the time taken to travel, the terrain, and any changes in speed or direction during the journey. Other factors such as traffic, weather conditions, and the type of transportation can also impact average speed.