What is the Average Speed Computation Problem on a Hill?

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SUMMARY

The Average Speed Computation Problem on a hill involves understanding that average speed is calculated as total distance divided by total time. In the example provided, a car travels up a 10 km hill at 10 km/h and down at 30 km/h, leading to a total distance of 20 km. The misconception that average speed can be simply calculated by averaging the two speeds (20 km/h) is clarified; the actual average speed is lower due to the longer time taken to ascend the hill. This problem highlights the importance of considering time intervals when calculating average speed in scenarios with varying velocities.

PREREQUISITES
  • Understanding of basic physics concepts, particularly speed and velocity.
  • Familiarity with the formula for average speed: total distance / total time.
  • Knowledge of how to calculate time based on speed and distance.
  • Ability to analyze scenarios involving different speeds over the same distance.
NEXT STEPS
  • Study the concept of average speed in varying conditions, focusing on different speeds over equal distances.
  • Learn about the implications of time intervals in speed calculations.
  • Explore real-world applications of average speed in physics problems.
  • Investigate related problems in kinematics that involve acceleration and deceleration.
USEFUL FOR

Students studying physics, educators teaching kinematics, and anyone interested in understanding the principles of average speed in real-world scenarios.

Bashyboy
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Homework Statement


The problem is in the provided link (it is questions 2.2) http://www.docstoc.com/docs/3817109/Chapter-Problems-A-car-travels-up-a-hill-at-a


Homework Equations





The Attempt at a Solution


I understand the duration of time it takes to go up the hill is a larger time interval than going down; but I fail to see that fact as a viable way to justify not just simply adding the to velocities and dividing by two. Could someone please understand this part to me, thank you.
 
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Bashyboy said:

Homework Statement


The problem is in the provided link (it is questions 2.2) http://www.docstoc.com/docs/3817109/Chapter-Problems-A-car-travels-up-a-hill-at-a


Homework Equations





The Attempt at a Solution


I understand the duration of time it takes to go up the hill is a larger time interval than going down; but I fail to see that fact as a viable way to justify not just simply adding the to velocities and dividing by two. Could someone please understand this part to me, thank you.

Average speed is total distance / total time. The length of the hill enables us to calculate the time for the trip - and has no other application.

Perhaps an example is easier explanation.

Suppose the hill is 10 km long, and you travel up at 10 km/h and down and 30 km/h

You are tending to an answer of 20 km/h for the average speed.

The total trip (up then down) is 20km. At 20 km/h that would take 1 hour

HOWEVER: If traveling at 10km/h on the way up, it takes 1 hour to get up the hill, so it is impossible to get up and down in 1 hour - so to simply add the velocities and divide by 2 doesn't work.

The simple average only applies if you travel at different speeds for equal times.

40 kph for 1 hour then 60 kph for 1 hour means an average speed of 50 kph
Note that you covered 40 km in the first hour then 60 km in the second hour - so it can't have represented a trip in opposite directions along the same piece of road.
 
That was bloody brilliant, thank you so very much for taking your time to answer my question.
 

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