• LOGIN
  • No products in the cart.

Profile Photo

Power and Acceleration

Assume that a constant power P is supplied to an electric train and it is fully used in accelerating the train. Obtain relation giving the velocity of the train and distance travelled by it as functions of time.

Solution:

We know, power (P)= force(F)*velocity (v).

Therefore,

m dv/dt=P/v

or, vdv=P/m dt

Integrating both sides, we have

∫vdv= P/m ∫dt

v2/2=P/m t+c

where c is a constant of integration.

Now, at t=0, v=0 so c=0.

Therefore,

Or, v = √(2Pt/m)……… (i)

We know, v= dx/dt

So, from equation (i)

dx/dt= √(2Pt/m)

Integrating both sides,

∫dx= √(2Pt/m) dt

or, x= (2/3)√(2P/m)t3/2

 

May 30, 2017

No comments, be the first one to comment !

Leave a Reply

Your email address will not be published. Required fields are marked *

© Cheenta 2017

Login

Register

FACEBOOKGOOGLE Create an Account
Create an Account Back to login/register
X