1. Assuming an average car weighs around 4000 pounds
2. Force required to move such a car (neglecting friction):
F = ma
As per the above,
m = 4000 /2.2 kg [approx. 1800 kg] a = 1 m/sec^2
=> F = 1800 N
3. Since it would be next to impossible to get a rare earth magnet that produced that kind of force, we would be, better served trying to use a solenoid. The formula to get the force generated by a solenoid is given by:
F = ((N * I) ^ 2 * k * A) / 2 * g ^ 2
Where,
N - No of turns
I - Current in Amps
k = 4 * pi * 10 ^ -7 (constant)
A - Cross-section of the solenoid
g - distance between solenoid and the metal that needs to be attracted
From the above, assuming a cross section of 0.5 sq m (A), current of 10 A (I), and a distance of 1 m from the solenoid (g), the number of turns required to produce 1 m/sec^2 acceleration on a 1800 Kg car is,
N ~= 7.568 * 10 ^ 3 ~= 7000 turns
Now, Density of Copper is 8.92 gm/cm3. We can guesstimate the weight by guessing the length of such a solenoid.