Cheenta
How 9 Cheenta students ranked in top 100 in ISI and CMI Entrances?
Learn More

Power and Acceleration

Let's discuss a beautiful problem useful for Physics Olympiad based on Power and Acceleration.

The Problem: 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 traveled 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

Knowledge Partner

Cheenta is a knowledge partner of Aditya Birla Education Academy
Cheenta

Cheenta Academy

Aditya Birla Education Academy

Aditya Birla Education Academy

Cheenta. Passion for Mathematics

Advanced Mathematical Science. Taught by olympians, researchers and true masters of the subject.
JOIN TRIAL
support@cheenta.com