You have two speeds at the same time ?jnuz73hbn said:Homework Statement: Hello, I have 2 speeds and need to calculate the average speed during the time traveled
i know that, but I only have two 2 speeds for a car, 60kmh in the first half of the journey and 115km/h in the second halfDaveE said:You haven't really stated the full question. Average is a mathematical operation that can be applied to different problems in different ways. So, this may make sense if you are asking about the average result from a bunch of separate cars on a race track. But for one car driving on a highway the average speed for the whole trip is calculated from the total distance divided by the total time. For example suppose I can drive for 10 minutes at 60mph (=10 miles) but then have to drive for 50 minutes at 30mph (=25 miles). My average speed would then be 35 miles in 1 hour.
Always start with the definitions. What is the definition of average speed?jnuz73hbn said:only one object that first moves at $$60km/h$$ and then at $$115km/h$$
$$ v= \frac{s}{t} $$ but I dont have $$s$$ I only have two 2 speeds for a car, 60kmh in the first half of the journey and 115km/h in the second halfharuspex said:What is the definition of average speed?
"half of the journey" is an important piece of information. Make up a value for total length for the trip and do the calculation. Then try it again for a different choice of total length. Does the length matter?jnuz73hbn said:i know that, but I only have two 2 speeds for a car, 60kmh in the first half of the journey and 115km/h in the second half
Nothing is given about the route, you should only calculate using this information. It means half of the time.DaveE said:"half of the journey" is an important piece of information. Make up a value for total length for the trip and do the calculation. Then try it again for a different choice of total length. Does the length matter?
Or maybe "half" means half of the time. Try with different total times for the trip.
The route doesn't matter. Turns don't matter. The only variables that go into a speed calculation are distance and time.jnuz73hbn said:Nothing is given about the route, you should only calculate using this information.
If you drive halfway round a racetrack at a speed of 60 km/h and at a speed of 115 km/h for the the second half, then the average speed is not ##\frac{60 + 115} 2## km/h. That a common mistake.jnuz73hbn said:i know that, but I only have two 2 speeds for a car, 60kmh in the first half of the journey and 115km/h in the second half
"Half the journey" is not very specific. It could mean "half of the time" or "half the distance". Each of those will give different results for the average speed. You need to specify which one you mean.jnuz73hbn said:$$ v= \frac{s}{t} $$ but I dont have $$s$$ I only have two 2 speeds for a car, 60kmh in the first half of the journey and 115km/h in the second half
but look, at the half of the driving time, speed is 60km/h, in the second half driving time, speed = 115km/h.PeroK said:If you drive halfway round a racetrack at a speed of 60 km/h and at a speed of 115 km/h for the the second half, then the average speed is not ##\frac{60 + 115} 2## km/h. That a common mistake.
first half of time=60km/h; second half of time is 115km/hOrodruin said:"Half the journey" is not very specific. It could mean "half of the time" or "half the distance". Each of those will give different results for the average speed. You need to specify which one you mean.
So, if the journey takes two hours, then the first half of the journey is 60 km and the second half of the journey is 115 km?jnuz73hbn said:first half of time=60km/h; second half of time is 115km/h
So, assume that the full time is ##T##. How far do you get in the total journey? The average speed is that distance divided by ##T##.jnuz73hbn said:first half of time=60km/h; second half of time is 115km/h
is this new formula correct?Orodruin said:So, assume that the full time is ##T##. How far do you get in the total journey? The average speed is that distance divided by ##T##.
For the other case, assume that the total distance is ##D##. How long will it the journey take travelling ##D/2## at the first speed and then ##D/2## at the second speed? The average speed is then ##D## divided by that time.
I suggest you perform both of these computations to find out that the result is not the same.
That is correct if the two distances are the same. This expression is known as the "harmonic mean".jnuz73hbn said:$$t_1=\frac{D/2}{v_1}$$
that means:
$$v=\frac{2}{1/v_1+1/v_2}$$
For the case of travelling half the distance at each speed, yes. Note that it can also be written:jnuz73hbn said:is this new formula correct?
The formula to calculate the average speed given two speeds \( v_1 \) and \( v_2 \) over the same distance is: \( \text{Average Speed} = \frac{2 \cdot v_1 \cdot v_2}{v_1 + v_2} \).
The arithmetic mean of two speeds does not account for the time spent traveling at each speed. The harmonic mean is used instead because it properly weights the speeds based on the equal distances traveled at each speed.
If the distances traveled at each speed are equal, the harmonic mean formula can be used. If the distances are different, the average speed must be calculated by considering the total distance and total time taken.
Sure! If a car travels at 60 km/h for half the distance and 40 km/h for the other half, the average speed is calculated as follows: \( \text{Average Speed} = \frac{2 \cdot 60 \cdot 40}{60 + 40} = \frac{4800}{100} = 48 \) km/h.
If the two speeds are the same, the average speed is simply equal to that speed. For example, if both speeds are 50 km/h, the average speed is also 50 km/h.