A car accelerates from rest to a certain velocity in a certain time. Assume that there is no friction, and that the engine power is constant. Consider the following scenarios independently. How long would it take to reach double the velocity (also from rest)

it will take half of the initial time to reach double the velocity

Explanation:

Given that a car accelerates from rest to a certain velocity in a certain time.

Since the car accelerate from rest, the initial velocity U = 0

Using the first equation of motion,

V = U + at

V = at

Assume that there is no friction, and that the engine power is constant. Consider the following scenarios independently. How long would it take to reach double the velocity (also from rest)

That is V = 2V

Using the same formula ,

2( at ) = at

2T = t

T = t/2

Therefore, it will take half of the initial time to reach double the velocity

the minimum amperage that the current in this wire would have to have so that its weight is completely supported by the magnetic force due to earth's field, assuming that no other forces except gravity act on it

this would be about 43%