INTRODUCING 5 - days-a-week problem solving session for Math Olympiad and ISI Entrance. Learn More

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

v^{2}/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)t^{3/2}

Advanced Mathematical Science. Taught by olympians, researchers and true masters of the subject.

JOIN TRIAL
Google