Power Problem: Accelerating a Car over Track Distance

[twituksh12345]

Homework Statement

A funny car accelerates from rest covering a particular track distance in time T.The engine of the car supplies a constant power of P for the entire time T. Now, the power is increased by a small amount dP. The power P+dP is kept constant for the entire track distance.What is the change in the time, required to cover the track distance with the new increased power?

Homework Equations

The Attempt at a Solution

 

[LowlyPion]

Homework Statement

A funny car accelerates from rest covering a particular track distance in time T.The engine of the car supplies a constant power of P for the entire time T. Now, the power is increased by a small amount dP. The power P+dP is kept constant for the entire track distance.What is the change in the time, required to cover the track distance with the new increased power?

Homework Equations

The Attempt at a Solution

Welcome to PF.

How would you approach the problem?

What is the relationship between power and acceleration?

 

[rl.bhat]

Power P = F*s/T where s is the distance of the track.
SO p = m*a*s/T
If car takes time T to cover distance s, then s = 1/2*aT^2 or a = 2S/T^2. Substituting this in p we get
P = 2ms^2/T^3. Hence for a given mass and distance, P = k/T^3
Now find dP/dT and find dT in terms of P, dP and T.

 

[twituksh12345]

thank you very much for yr reply.
The solution that you provided gives the corect answer.
But, i do not understand one thing--
P= F.v
Now, since the car accelerates, v is not constant.
But as the power is constant, F should also vary.
Since mass is constant and F varies, acceleration should vary.
Under the conditions of changing acceleration, s=1/2at^2 is not true.
So, is it correct to apply the formula-- s=1/2at^2?