Electric motors and amps. Project time?

The motor ratings and their relationships are volts (maximum speed) amps (maximum torque), and power which is the full load mechanical output. The electrical input power is more than the mechanical power, according to the efficiency, which could be 80% for these at a guess. Power is proportional to rpm and torque, and also volts * amps.

The current the motor draws depends on the mechanical load. With an ideal motor and no load it would be negligible. This is inherent. Increase the load and the current increases. The voltage is varied to adjust the speed, though this can be modified to automatically control torque and current to some limited value. Motors need to be protected against overcurrent, so they do not burn out when overloaded. This usually involves a time aspect as well as current. If the load is too much for too long, the motor gets too hot. A simple control is an ammeter with a red line for the operator. On a scooter the motor can probably be made big enough that just a circuit breaker/fuse can protect it, because the usual person would not be silly enough to use the full power, too scary. However a speed controller can easily be adapted to add current protection.

The power required from the motor depends on several different scenarios. Acceleration, hill climbing and overcoming rolling friction and drag at a given speed. The minimum power is required when cruising along on a flat road at a moderate speed to minimise friction. The maximum power occurs when trying to accelerate strongly and climb up a hill, especially if the speed (and so friction/drag) is already high. The power for cruising at full speed is probably not much above minimum power for a scooter, as the air drag is not very high at the low speeds involved. The additional power the motor can produce is to provide reasonable hill climbing and acceleration, as well as allowing it to operate on a less suitable surface like softer ground.

You will only draw full power during acceleration or going up a hill. The 7 amps you mentioned is probably while cruising on level ground which only requires 250 watts

7A is the average load for motor while running smoothly at full speed . At its full speed,motor generates quite a big counter emf to make it uses less current ( most efficient way to operate a motor ). Do not forget while motor at start,it requires a lot of start up current could reach close to its current limit 18A. Same situation is applied while it climes up hill at low speed high torque.

Suppose a designer like you without knowing this facts and make the motor running at 18A at full speed. This motor will burn down either during start or running on low speed.

The motor current depends on the torque requirement. On a flat surface at a constant velocity the current (torque) may be less than the full load capability. If the motor has to accelerate, the torque (current) will increase.