How is the speed controlled on an electrical DC (or AC) motor? I'm sure I've heard that a motor will almost instantly reach full speed and this would be a problem in electric cars or even remote control ones, so I was wondering what components have to be used to solve this problem to allow the speed to gradually increase or to be adjusted in the case of an electric vehicle?
You need to specify the type of motor you are going to use. Every different type needs a different approach to speed control. If you want to use a universal motor then continuous speed control of a universal motor running on AC is very easily accomplished using a thyristor circuit, while stepped speed control can be accomplished using multiple taps on the field coil. In the case of synchronous motors you might not be able to change the motor speed. As for connecting the wheel. You might be able to use chain drive. Sprockets on both wheel and motor shaft and link with chain. Possibly you could use a belt. You would need something like a vee pulley on each.
En electric motor in an electric car is controlled by a controller. Simple enough... The controller limits power to the motor by sending signals to turn the motor on and off at varying intervals to give the function of speed. A typical EV controller will turn the motor on and off in segments of thousandths of a single second.
The output speed of the motor depends on the amount of current passing through it. What you are thinking of is the torque of an electric motor, unlike a reciprocating engine an electric motor produces max. torque however fast the motor is turning. To control speed you would use some kind of variable resistor which would allow you to alter the current passing through it. Hope this helped :)
Depends on the kind of motor. For a stepper motor the actual position of the shaft can be controlled, so you adjust the rate of change of position. For a synchronous AC motor, you could change the frequency of the supply. For other types you would adjust the current through the windings with an electronic controller. Using a variable resistor is inefficient since significant power is dissipated in the resistor. I believe one would normally use pulse-width modulation to change the average current not peak current.