Calculating Average Velocity of a Moving Train: Solving Kinematics Problem

In summary, the conversation discusses the problem of finding the average velocity of a train on a route with varying acceleration and deceleration. The formula v(avr) = v/(1+(v^2)/as) is given, but the steps to reach it are unclear. The relationship between acceleration, velocity, and time is discussed, and the formula d=(v^2)/2a is used to determine the distance traveled. By drawing a velocity vs. time graph, the distance covered during each segment can be visualized.
  • #1
Hassin
3
0
Hello, I have problem with this example. I don't speak English very well, so please forgive me if something isn't quite enough defined - as it should be in English Physics terminology.

The train moves from the station with an acceleration a. After reaching velocity v moves farther with constant velocity, next train moves with deceleration and, at last to dwell on the following station. What is the average velocity of the train v(avr) on the rout in length s?

I know that the answer should be v(avr) = v/(1+(v^2)/as). But I don't know how to get to it. Could somebody tell me step by step what should I do?
 
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  • #2
You didn't specify the deceleration rate, but from the answer it looks as though that is also a (or rather, -a). Suppose the acceleration lasted time t.
What is the relationship between a, v and t?
How far did it travel while accelerating?
How long did it spend decelerating?
How far did it travel while decelerating?
So how far did it travel at speed v?
So how long did it spend at speed v?
So how much time did the whole journey take?
 
  • #3
Let the magnitude of acceleration and deceleration is equal to a

Let d the distance traveled both acceleration and deceleration

d= v2/a
s=d+Tv, Time for constant velocity

T=s/v - d/v= s/v-v/a

Vav=s/(T+2v/a)

Vav=s/(s/v-v/a+2v/a)

Vav=s/(s/v+v/a)

Vav=s/((sa +v2)/va)

Vav=sav/(sa +v2)

Vav=v/(1 +v2/sa)
 
Last edited:
  • #4
Thank you very much, I didn't know this formula without time d=(v^2)/2a.
Very helpful :)
 
  • #5
By drawing a velocity vs. time graph, you can easily see the distance covered every segment.
 

What is kinematics?

Kinematics is the branch of mechanics that studies the motion of objects without considering the forces causing the motion.

What is average velocity?

Average velocity is the total displacement of an object divided by the total time taken. It is a measure of an object's overall motion over a given period of time.

How is average velocity calculated?

Average velocity is calculated by dividing the change in displacement by the change in time. The formula for average velocity is:
Average velocity = (final displacement - initial displacement) / (final time - initial time).

What are the SI units for average velocity?

The SI units for average velocity are meters per second (m/s).

How is average velocity different from instantaneous velocity?

Average velocity is calculated over a given period of time, while instantaneous velocity is the velocity of an object at a specific moment in time. Average velocity takes into account the overall motion of an object, while instantaneous velocity focuses on the object's velocity at a single point in time.

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