How Does Increasing Engine Power Affect Race Time for a Funny Car?

[vebes02]

Homework Statement

A funny car with mass of m accelerates from rest through a measured track distance D with the engine operating at a constant power P. If the track crew can increase the engine power by a differential amount dP, what is the change in the time required for the run? Express your answer exactly in terms of the variables given.

Homework Equations

P = W/t
P = dW/dt

The Attempt at a Solution

I know the problem is asking for dT, but I just don't know how I would single it out. So far I've got: dT = ((dP+ P) - P)/ m * (dV/dt) * Dx which I know is not right. Any suggestions would be helpful.

 

[tiny-tim]

Hi vebes02!

Find the equation relating P and t, then just differentiate it …

what do you get? ​

 

[tomcue]

I would approach this question by first identifying the relevant equations and variables. From the given information, we can use the equation P = W/t, where P is power, W is work, and t is time. We can also use the equation P = dW/dt, where dW is the differential change in work and dt is the differential change in time.

Next, we can use the equation for work, W = Fd, where F is force and d is distance. In this case, the force is the force of the engine, which we can assume is constant, and the distance is the measured track distance D.

We can then combine these equations to get P = Fd/t. Since we are looking for the change in time, we can rearrange this equation to get dt = d/Fd * dP, where dP is the differential change in power and d is the distance D.

Therefore, the change in time required for the run would be dt = d/Fd * dP. We can express this in terms of the given variables as dT = D/(F*D) * dP. This means that for every unit increase in power, the time required for the run will decrease by D/(F*D).