If there was no air resistance, would a car have constant acceleration with constant air/gas input? To get from 0 to 50 m/s takes a certain amount of force. To get from 50 to 100 takes equal force over equal time, but takes more energy, so would it take more gas input for the second half, meaning the force would slowly decrease as it accelerates leading to a longer time taken to get up to speed if gas input was not changed? I always thought it was air resistance or the gears maxing out that made it take longer to get from 50 to 100 kmh, for example, than it did to get up to 50 from 0.
 A: If the car has an ideal continuously variable transmission (so that the engine can always deliver its full power to the wheels), and infinitely sticky tires (so that they don't spin out at the beginning), and you don't consider drag or any other real-world factors, then the kinetic energy of the car increases at a constant rate.  That rate is the power of the engine.  Speed would increase proportional to $\sqrt t$, so it would take exactly three times as long (also three times as much gas/air) to go from 50 mph to 100 mph as to go from 0 mph to 50 mph. 
Even with all the real-world factors added back in--air resistance, transmission, tires, etc.--the fact that a car going 100 mph has four times the kinetic energy than one going 50 mph is a major factor in why it takes so much longer to go 50-100 than 0-50. Engines can only spin so fast--you can't hit 100 mph in first gear. When you shift up, the engine still puts out the same amount of power, but the higher gear ratio means that the force transmitted to the road is less. Plenty of cars can transmit enough force to cause the drive wheels to slip on the asphalt in first gear.  Very few can do so in fifth gear (or even third). So as you approach 100 mph, your acceleration is a lot less than when you started.  Air resistance just increases the effect.
A: No. There are other non-linearly related opposing forces such as bearing friction for instance. And the friction between the tire and the road.
A: Let's consider the logic in your question vs the physics. Given no air resistance from air, no engine internal resistance, no drive system parts resistance:


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*"To get from 0 to 50 m/s takes a certain amount of force. To get from 50 to 100 takes equal force over equal time, but takes more energy..." This is true. Acceleration = Force/Mass. At constant force and mass, acceleration remains the same. Time = (change in Speed)/Acceleration, so time is the same. Distance = (average Speed) x time, and average speed will increase, and consequently, so will distance covered. Energy = Force x Distance, so energy required will increase.

*"...so would it take more gas input for the second half, meaning the force would slowly decrease as it accelerates leading to a longer time taken to get up to speed if gas input was not changed?..." Well, assume the force stays the same, because it generally can. However, gasoline input per second would have to increase because the mass of the car is being pushed a greater distance per unit time during the 50-100 m/s acceleration. The force acts over a longer distance.

*The moral of the story is that displacement under force (in this case required to overcome the tendency of the car mass to resist acceleration) requires energy. If there is no resisting force to overcome, no energy is required during cruising (constant speed). This is the appeal of Hyperloop.


For the case including air resistance, engine friction losses, drive train losses, then it is easy to show that air resistance and friction losses are higher at a higher speed.
A: An alternate equation for power is $P=Fv$. If the power output of the engine is constant, as the velocity increases, the force on the car must decrease. According to Newton's 2nd law, $F=ma$, meaning that the acceleration decreases as the velocity increases. This means that the car will take longer to go from 50 m/s to 100 m/s than it took to go from 0 m/s to 50 m/s. 
A: Consider a thought experiment that I think will tap into your intuition. 
You have a car on the road, and on its roof you have an extremely long platform (like an aircraft carrier runway), with another car on that runway. Both cars are going to travel in the same direction.
We'll disregard the engineering challenge of this, and assume that the runway supported by the lower car is sufficiently long for the upper car to travel quite some distance along it. We'll also disregard any effects of drag caused by the air or by mechanical parts, and we'll assume the runway is more or less weightless (so the only things with substantial weight are the cars and the drivers in them).
Now the driver of the lower car puts their foot down, and brings the whole setup up to 50mph (obviously, carrying the weight of both cars means he burns twice as much fuel in this step). So now both cars are travelling at 50mph relative to the ground, and the upper car is travelling at zero mph relative to the runway.
Being in a dragless environment, this entire setup will cruise at 50mph with no further energy input - the lower driver could turn his engine off, if he wished to, and both cars would sail off into the sunset. 
Now let's move to the driver in the upper car on the runway. Since he is already doing 50mph relative to the ground, it follows that he can put his foot down, and when he reaches 50mph on the runway, he will be doing 100mph relative to the ground, yes?
So the upper car sets off. But when he puts his foot down, the lower car carrying the runway slows down relative to the ground almost as much as the upper car gains relative to the runway! It's like the runway is sliding out from beneath him, so that when he gets up to 50mph relative to the runway, the runway itself (and the lower car) has stopped relative to the ground, and the upper driver is therefore still only doing 50mph relative to the ground! 
In other words, the entire energy input from the engine of the upper car, even though he's speeding along the runway at 50mph, went into slowing the runway down whilst the upper car maintained it's steady speed relative to the ground. He's had his foot down for several seconds, and hasn't gained any extra speed relative to the ground!
What this shows is that, once the lower driver has brought the entire setup up to 50mph, in order for the upper car to accelerate relative to the ground, both drivers have to keep their foot on the gas in equal amounts - the upper car puts his foot on the gas in order to move along the runway, and the lower driver puts his foot on the gas to make sure the lower car which supports the runway maintains its 50mph speed relative to the ground, against the push of the wheels of the upper car. So now you've got two engines working equally, just to accelerate the one (upper) car (the lower car's engine has to work purely to maintain its speed against the forces exerted by the upper car against the runway).
In theory without drag, the cars could be geared such that they could accelerate almost indefinitely, but each time the engine is further overdriven by gearing, the amount of torque at the wheels reduces, so that eventually their acceleration (despite being at full throttle) would slow to an infinitesimal crawl, because the engine has a fixed maximum energy output.
And somewhere in this scenario, is the explanation for why it takes significantly more fuel to get from 50mph to 100mph, as to get from 0mph to 50mph. And in fact, from 0mph to any given speed, each doubling of the speed, takes twice as much energy again, as the energy required to attain the speed already gained. 
So getting to 50mph does not take 50 times the energy it took to get to 1mph - it takes millions of times more energy than what it takes to get to 1mph.
The beneficiary of all this extra energy input is the crust of the Earth itself, which is given up again (mostly into heat and the chemical and structural breakdown of the brake pads and discs) when the car slams on its brakes. 
It seems like a counter-intuitive situation, but it is completely familiar to our everyday experience. It takes twice as much energy to get up to a running pace as to get up to a walking pace, and twice as much to stop again (since humans don't have separate "braking parts" like cars, and it mostly has to be done with muscle power).
It's simply by convention that we use linear speedometers rather than logarithmic ones, so that a linear increase in the numerical speed involves an exponential increase in energy. Other aspects of human senses are similar - for example, with our hearing, a doubling in the perceived loudness of a sound, actually involves an exponential increase in the power of the sound wave.
