# Vehicle Acceleration Curve

I am programming a game in which there are no outside forces acting on the car aside from the engine. I will not be having gears, so that is not a factor. I just want to know if there is an equation I can use to calculate the car's speed at any given time. The car will start off accelerating quickly, but then as it approaches top speed, it will accelerate slower and slower until it reaches top speed. Also, finding the car's 0-60 time is easy, just a google search, but because of this curve, that does not give me the original speed. Is there a way to figure that out?

The car's stats are:
0-60 in 4.5 seconds
Top Speed: 155 MPH

Please show your steps so that I can replicate it for the other car types in my project.

The car will start off accelerating quickly, but then as it approaches top speed, it will accelerate slower and slower until it reaches top speed.
That may depend on how it accelerates or decelerates. So, if you want to accurately get the speed of any time, the change of acceleration should also be given.

SteamKing
Staff Emeritus
Homework Helper
Also, finding the car's 0-60 time is easy, just a google search, but because of this curve, that does not give me the original speed. Is there a way to figure that out?

The car's stats are:
0-60 in 4.5 seconds
Top Speed: 155 MPH

Please show your steps so that I can replicate it for the other car types in my project.

What do you mean by the original speed?

FactChecker
Gold Member
Use a constant engine force Fe opposed by a drag force Cd * velocity2. Since the top speed is 155, you know that the engine force and drag force are in balance at 155 mph. So Fe-Cd*1552 = 0. and Cd = Fe/(1552). You also know the time to 60 is 4.5. So the second integral of (Fe - Cd*velocity2) = Fe * (1-(velocity/155)2 over 4.5 seconds is 60. You can calculate Fe and then Cd from that.

PS. The zero to 60 mph times from Google searches are certainly for a standing start.

• pacificapilot
What do you mean by the original speed?
Original as in the starting speed, which, in this case, is 0 mph

Use a constant engine force Fe opposed by a drag force Cd * velocity2. Since the top speed is 155, you know that the engine force and drag force are in balance at 155 mph. So Fe-Cd*1552 = 0. and Cd = Fe/(1552). You also know the time to 60 is 4.5. So the second integral of (Fe - Cd*velocity2) = Fe * (1-(velocity/155)2 over 4.5 seconds is 60. You can calculate Fe and then Cd from that.

PS. The zero to 60 mph times from Google searches are certainly for a standing start.
Thanks!