ABS comes on during acceleration

there are wheel sensors and the job of your computer to sort these signals out...apply brakes to stop you from skidding...no kidding~ either go with it, take it in to have either the sensors inspected and wiring replaced as needed or go right ahead into an out of control skid~

Repair shops have a scanner to read the ABS system. They can tell you what part has failed and the cost of repair.

It's possibly the traction control being messed up, on the late model Land/Range Rovers TC works by braking a spinning wheel to provide torque to the wheel that has traction. If it has a problem and thinks it lost traction it can randomly actuate brakes which can really mess up the driveability and safety of the car. Get it checked out with a diagnostic computer soonest!