# Calculate acceleration of a vehicle.

1. Jan 20, 2005

### nazo

hello,

i need to calculate acceleration of a vehicle. I have power (70 bhp), Tractive force (498N). Can someone help me please. I know i should use dv/dt but i cant remember how to do differential equations.

Also I need the formula to include downforce as I am designing a rear wing. does someone know the formula.

thanks.
Nazario.

2. Jan 20, 2005

### dextercioby

For the first part,are u sure this is all the data??
I men,u have the force,u need the mass.Unfortunately,the engine power will give the product between the tractive force and the velocity.So u can find the velocity.But i can't see a way of finding the acceleration...

Daniel.

3. Jan 20, 2005

### nazo

i have the weight 375 kg, i need the force... hmm... i onloy have tractive force. i might need the total force. how do i do that?

thanks.

4. Jan 20, 2005

### Staff: Mentor

Initial acceleration is always easy: its determined by the traction (since virtually any car is capable of spinning its wheels). a=f/m

After that (basically, after shifting out of first gear), you need the engine torque (or, more useful, torque at the wheel) - convert that to force and apply f=ma again and you can get an acceleration curve.

Downforce does not affect acceleration except in that it creates drag. And adding drag to this question makes it very complicated (and probably not solvable without a wind tunnel). Dynamic forces inside the drive-train (angular acceleration of the components) also complicates things.

Last edited: Jan 20, 2005
5. Jan 20, 2005

### Andrew Mason

The acceleration has to be a function of time because the rate of power loss due to friction is a function of speed (ie. d/dt(P_f) = d/dt (F*s) = F ds/dt = Fv)
So use:
$$F*v = P$$

Since the force is: $F = ma + \mu_kmg$ and v = at you have:

$$P = Fat = ma^2t + \mu_kmgat$$

You should be able to solve this quadratic equation for a (in terms of t). The acceleration will decline until the power output (Fv) is equal to the friction force * v.

AM

Last edited: Jan 20, 2005