Let’s ignore car 1 'cos we know that was doing 40 and ended up doing 60.

Car 2 went from 0 to ?? over 0.2 miles starting at 40 mph = 0.011 miles/second

Newtonian law states final speed = initial speed + acceleration x time

We don’t know acceleration, so assume 0-60mph (0-0.016mps) in 10 seconds:

speed = acceleration x time

so

acceleration = speed/time so 0.016/10=0.0016 miles per second per second

So now:

final speed = initial speed + acceleration x time

= 0.011 + (0.0016 x 8)

= 0.0238 miles per second

= 85.68 miles per hour

The stats for car 2 are:

It covered 0.1 miles at 0.011 miles per second (40mph) which would have taken it 9.09 seconds

It therefore accelerated from 40 to 60 in 3.1 seconds over 0.1 miles

From Newtonian Law at can be derived that (final speed(squared)) - (initial speed (squared)) = 2 x acceleration x distance

Or in this case

(0.016x0.016) - (0.011x0.011) = 2 x acceleration x 0.1

0.000256 - 0.000121 = 0.000135 = 2 x acceleration x 0.1

so

0.00135 = 2 x acceleration

and

0.000675 miles per second per second was the acceleration achieved.

Thats after 18 pints so the sums may be dodgy but the equations were drummed into me over years and I can still prove them with pencil and paper so trust me they are right:)

this is more of a physics question, i cant quite understand what your after but surely it’ll require the equations of motion which is what mojo used above
there all here
hope that helps
Bully

Of course all of the above assumes that acceleration is constant. In the real world this doesn’t tend to be the case.

Rate of acceleration for a car is determined by balancing power at the wheels against drag (both aerodynamic and mechanical although aerodynamic drag dominates). Power at the wheels varies with engine (and therefore vehicle speed) speed as does drag.

In simple terms, acceleration is at it’s highest at low speeds and tends towards zero as you get closer to the vehicles maximum speed.

It’s all a bit complicated to calculate this kind of thing accurately however if you’re prepared to make a few assumptions (such as constant acceleration) it gets alot simpler.

If you want to get a feel for some real figures have a look for a program called ‘cartest’ and play with that for a bit.