I am a high school physics student and I've been trying to simulate the acceleration of a car as it fully accelerates from rest, but I'm finding it's much harder than I thought. Here was my first attempt (without including air resistance):

I used the horsepower to calculate the kinetic energy of the car since power = $\frac{\Delta E}{\Delta t}$ and in this case $E$ is the kinetic energy of the car. I substituted this into $KE = \frac{1}{2}mv^2$ and after manipulating the equation I ended up with:

$$v(t)=\sqrt\frac{2\dot{}hp\dot{}t}{m}$$

After taking air resistance into account, I substituted actual hp and mass of a Ferrari and took the limit as $t\rightarrow \infty $. My simulated top speed was very close to its actual top speed, but something wasn't right. The acceleration curve is decaying and at $t=0$ acceleration is infinite. 

[One source](https://youtu.be/eUHOx-_1xZc?t=8m3s) tested the acceleration of a few super cars from 0 to 60 and the acc vs time curve looks like this:[![enter image description here](https://i.stack.imgur.com/vOe20.jpg)](https://i.stack.imgur.com/vOe20.jpg) After more research, I figured I must take into account torque, gear ratios, and RPM, but it only confused me more. Does anyone have any insight to make a realistic simulation, what equations to use, or which properties of the car are relevant? One car I would like to use for the simulation would be the [Koenigsegg Regera](https://en.wikipedia.org/wiki/Koenigsegg_Regera) because it has one fixed gear, which I thought could make calculations more simple. Thanks for any help or advice.

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(Update)

Thanks to previous answers, I have found out that I can use a torque curve to relate the engine's RPM to torque, and thus solve for acceleration. The only problem that remains is how to find the rate of change of engine rpm. Consider a car at rest is running at 1000 rpm. If the driver then completely floors the throttle, how would I figure out how fast the rpm increases and approaches redline? To my current understanding, I need this information to find the torque at any given moment.