Calculating Average Speed: Mobile's Trip

In summary, the problem involves a mobile moving in two portions, with the first portion being 10% of the total distance at a speed of 10 m/s and the second portion being the remaining 90% of the total distance at a speed of 30 m/s. The task is to find the average speed for the entire trip, with the options of 25m/s, 22.5m/s, 20m/s, and 15m/s. The relevant equation is \Delta v = \frac{\Delta d}{\Delta t}, and the solution involves calculating the time for each portion, adding them together, and then dividing the total distance by the total time. The correct answer is 25m/s, but
  • #1
rAz:DD
11
0

Homework Statement


A mobile is moving straight as following: the first portion of the road, equal to 10% of the total distance with the speed v1=10/s , and the rest with the speed v2=30m/s.
The average speed for the entire trip is?
a)25m/s b)22.5m/s c)20m/s d)15m/s


Homework Equations



[tex]\Delta v = \frac{\Delta d}{\Delta t}[/tex]

The Attempt at a Solution



I calculated the times passed for both distances, replaced them in the average speed's formula and got 25 m/s, which is a wrong answer according to the key.
 
Last edited:
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  • #2
I think the key is wrong. The correct approach is as you described: calculate the time needed for each portion, add them together, and divide the total distance by the total time.

First part: dist = .1D, rate = 10 m/sec, time = .1D/(10 m/sec) = .01D
Second part: dist = .9D, rate = 30 m/sec, time = .9D/(30 m/sec) = .03D

Average speed = (total distance) / (total time) = D/(.01D + .03D) = D/.04D = 1/.04 = 25 m/sec.
 
  • #3
BTW, the equation you show as relevant is meaningless. dv is differential velocity and d/dt is the differentiation with respect to t operator. The first represents some quantity and the second indicates an operation to perform.
 
  • #4
Thanks for the answer
And sry for that dv/dt part, i wanted to type the greek letter delta and i didn't know whether tex codes are active or not.
 
  • #5
Yes, they are active. For the upper case delta (looks like a triangle), use \Delta
[tex]\Delta v = \frac{\Delta d}{\Delta t}[/tex]
 
  • #6
rAz:DD said:

Homework Statement


A mobile is moving straight as following: the first portion of the road, equal to 10% of the total distance with the speed v1=10/s , and the rest with the speed v2=30m/s.
The average speed for the entire trip is?
a)25m/s b)22.5m/s c)20m/s d)15m/s
Say the road is 100 m long. Then 10% is 10 m and, at 10 m/s, that requires 1 second. The second part is 90 m long and, at 30 m/s, that requires 3 seconds, making a total of 100 m in 4 seconds. That is an average speed of 25 m/s.


Homework Equations



[tex]\Delta v = \frac{\Delta d}{\Delta t}[/tex]

The Attempt at a Solution



I calculated the times passed for both distances, replaced them in the average speed's formula and got 25 m/s, which is a wrong answer according to the key.
What answer does the key give?
 
  • #7
The problem is here

v1=10/s

It's probably some really exotic unit of distance that was left out.

In other news, I'll second (or fourth at this point) the 25m/s crowd
 

Related to Calculating Average Speed: Mobile's Trip

1. What is average speed?

Average speed is the total distance traveled divided by the total time taken to travel that distance. It is a measure of the overall speed of an object over a certain period of time.

2. How do you calculate average speed?

To calculate average speed, you divide the total distance traveled by the total time taken to travel that distance. The formula is: Average Speed = Total Distance / Total Time

3. What units are used to measure average speed?

The most common units used to measure average speed are kilometers per hour (km/h) and miles per hour (mph). However, other units such as meters per second (m/s) and feet per second (ft/s) can also be used.

4. Can average speed be greater than the maximum speed?

No, average speed cannot be greater than the maximum speed. Average speed is calculated by dividing the total distance by the total time, and it represents the overall speed of an object. The maximum speed is the highest speed reached by the object at any given point in time.

5. How can average speed be affected by different speeds during the trip?

The average speed will be lower if there are significant differences in speed during the trip. For example, if an object travels at a high speed for half of the trip and then at a lower speed for the other half, the average speed will be lower than if the object traveled at a consistent speed throughout the entire trip.

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