Kinematics - average velocity

  • Thread starter Hassin
  • Start date
  • #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?
 

Answers and Replies

  • #2
haruspex
Science Advisor
Homework Helper
Insights Author
Gold Member
38,455
7,965
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
azizlwl
1,065
10
Let the magnitude of acceleration and deceleration is equal to a

Let d the distance travelled 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
Hassin
3
0
Thank you very much, I didn't know this formula without time d=(v^2)/2a.
Very helpful :)
 
  • #5
azizlwl
1,065
10
By drawing a velocity vs. time graph, you can easily see the distance covered every segment.
 

Suggested for: Kinematics - average velocity

Replies
2
Views
282
  • Last Post
Replies
3
Views
970
  • Last Post
Replies
2
Views
88
Replies
9
Views
498
Replies
1
Views
530
  • Last Post
Replies
5
Views
223
Replies
8
Views
86
Replies
2
Views
280
Top