Accleration Speed & Time

Ok so heres what I'm trying to figure out:
Given a required time i need to figure out how much wheel thrust is required to accelerate a car or truck to a given speed. (ie take a 5000 lb car to 75 mph in 15 seconds......)
I've been searching but cant find a good formula to use.

Pythagorean
Gold Member

f = dp/dt!!!! lol!

(note: lol is not a part of the formula)

could you break that down for me. what is dp and dt? and i'm thinking f is force?

I can find the G Force exerted on the car i just dont know how to turn that into time to a given speed

here is what i have so far
Givens:
Weight: 5000 lbs
Wheel Radius - 10 in
Tq @ Wheel 3000 ft-lbs

Calculated:
Wheel thrust = 3600 pound-force of thrust = .72 g

Last edited:
Let's break it down a bit. 75mph is 110 ft per second. If it takes 15 seconds to get to 75 mph, the vehicle experiences an average acceleration rate of 7.33 feet per second squared or about .23 gs. That means that your 5000 lb vehicle has to generate an average of 1140 lbs of thrust, or 950 ft lbs of torque at the axle shaft for your tire size.

If you could accelerate at a constant .72 g, you'd reach 75 mph in 4.74 seconds. Better dial up the boost!

thanks! actually I'm working on designing a EV truck with 6 150hp AC motors one on each wheel so making enough tq for 15 seconds is not a problem..... my problem is building a battery pack, Super Cap pack and generator to power it all.

Now how does this work if i start at say 25 mph and want to go to 75 mph with all the same numbers

F = MA so to accelerate at the same rate (A) you continue to apply the same force as calculated. BUT: only when air resistance and rolling friction becomes significant do you have to worry about "drag"...that depends on the shape of your car...but might be appreciable at maybe 40 MPH and up....

Well, since your change in speed is now 50 mph instead of 75 mph ...

This of course assumes that your acceleration rate stays constant, which it won't for a few reasons (two listed above) but I'm thinking that you're after a general trend rather than the exact numbers.

Yeah i know acceleration wont be constant but tq will remain constant thanks to nifty little devices called VFDs. like you said im just after the general numbers not the exact one. thanks for you help!