Should we use a Brushed or Brush-less DC motor to build a solar car?
Brushless motors are generally more efficient and so can make better use of the limited power available. However you still need to match the motor to the power source and load to get best efficiency. A few basic calculations can tell you what motor specs to look for:-  

First calculate what rpm the wheels must do to get the speed you want. A 12cm diameter wheel has a circumference of 0.377m. To get 2.5m/s linear velocity it needs to turn at ~400rpm.

Your motor has a Kv of 1400rpm/V, so if powered by 12V it should spin at ~12*1400 = 16800rpm without a load. Under load its speed will drop due to voltage lost in the resistance of the windings. Loading depends on a lot of factors such as rolling resistance, aerodynamic drag, bearing friction etc. however assuming you can get the motor running at peak efficiency its speed may drop to ~85% of no-load or 14000 rpm. Therefore you need a gearbox ratio of about 14000/400 = 35:1. 

The 1~1.5A maximum output current of your solar panels could be a problem with this motor because it draws over 1A just to turn over. Under acceleration it will try to draw even more current, but the solar panel may not be able to supply it so its voltage will drop and the speed controller might cut out. 

You should use a lower Kv motor that has smaller no-load current, eg. Scorpion SII-2212-885Kv which draws less than 0.5A at 12V. This motor only does about 9000rpm (12V * 885rpm/V * 85%) so for it you would need a 23:1 gearbox.