Powering a motor through wireless electricity
I figure this will be closed, but I'm going to answer anyway.  This is more in the way of things you need to do rather than a solution to your problem.


You need to find out how much power your motor needs to move the car. 


I assume it can move the car using a AA battery.

Measure the voltage across the motor while the car is moving.  It will be lower than 1.5V.

Now, measure the current through the motor while the car is moving.

Multiply the volts by the amperes (P=IE, power=current*volts.) This gives you the power in watts.

Your power transmitter/receiver system must be capable of transmitting at LEAST that amount of power.


Measure the power going into your transmitter. 


Place the transmitter/receiver coils together so that the receiver coil can receive maximum power.  Power up the transmitter, and measure the voltage across the battery, then the current flow from the battery.  Now, calculate the power going into the transmitter.  Your receiver will NEVER get more than this amount of power.

To increase the transmitter power, you need to give it more voltage or more current - or both.


Measure the received power. 


Hook up the motor to the receiver.  Leave out the LED.  It will only confuse you right now.  Measure the voltage across the motor and the current through the motor then calculate the power available to the motor.  

The difference between the transmitted power and the received power is the loss of the system. You can calculate the efficiency of the system as received power divided by transmitted power (Eff=Pr/Pt).  This number will be lower than 1.  A REALLY good system might reach 0.9 when the coils are close together.  I expect your number to be much smaller.

I expect will measure a received power that is much lower than the power the motor needs to move the car.

There are MANY things which can influence the efficiency of the system. One you already know - distance between transmitter and receiver coil.  But, the circuits have losses, and the coils have losses.  The coils must be matched to each other and to the circuits, else you will have losses between the coils and losses between the circuits and the coils.

You picked an interesting project, with a lot of things to learn and a lot of room for discovery.  It is also a difficult project - note that there are no existing systems that do what you are trying to do.  

If something hasn't been invented yet, there's often a good reason.  Either there's no basis to operate from (no body can figure out how it could be done) or the basis is well enough understood that engineers can calculate how well it would work before building one, and find that it wouldn't work well enough to be worth while.



If you have trouble carrying out any part of the above, ask your parents or teacher for help.  

You can also ask here, but then you must post a clear question that explains what you are trying to do and what you have done yourself to find the answer.  You will also need to post a drawing of your circuits illustrating your system and how you tried to make your measurements.

Do try searching the site here for basic questions.  Measuring voltage and current as well as calculating power are basic things that have been covered before.

The folks here like to help, but they are like your teachers - they want you to make an effort first.