# Acceleration using Power

1. Sep 1, 2004

### timman_24

I know acceleration can be found by the following basic equation:
A=F/M

But my question is can you also find acceleration using power or work?

Background:
I am doing a project in physics right now that involves taking the torque, weight, and drag of the car and calculating the theoretical 0-60, 1/4, and 1/8 mile times. The problem is cars are rated in horsepower (power) and torque (work.) I don't exactly know how to 1) Break them down to their force properties and solve or 2) make an equation that will solve for acceleration.

Can anyone help out?

2. Sep 1, 2004

$$F = ma$$

$$W = Fd$$

$$P = \frac{W}{t}$$

sub in Work into Power

$$W = Fd$$

$$P = \frac{Fd}{t}$$

since $$V = \frac{d}{t}$$

$$P = FV$$

play around with those, see what you get.

3. Sep 8, 2004

### timman_24

Well I messed around and got these... But it still isnt what I am looking for. Anyone else have some input?

$$P=FxTxA$$
$$P=pxA$$
$$P=MxVxA$$

I subed in momentum for $$FxT$$.
Then I subed in Mass and Velocity for Momentum...

Doesn't help me much, but it does get acceleration in the equation...

4. Sep 8, 2004

### krab

Nenad told you what how to get force from power: F=P/v. Use F=ma=dv/dt. You still need air resistance losses, and these are proportional to v^2.
$$m{dv\over dt}={P\over v}-kv^2$$
This gives v vs. t and you need to integrate once more to get distance vs. t.
You can get the proportionality constant k knowing the top speed and power, or the drag coefficient.

BTW, torque is not work.
BTW, given an adequate transmission, torque is a spurious performance parameter.

5. Sep 28, 2004

### timman_24

Okay I ended up getting power from velocity and air resistance using the drag formula:

[Tex]P=(cD)(A)(d)(v)^3[/tex]

Now what I need is not getting power from force but getting the accel from power. Anyone have any suggestions?

Thanks

Last edited: Sep 28, 2004
6. Sep 29, 2004

### krab

accel is dv/dt. Look again at the formula I gave. It is essentially ma=P/v-kv^2