What could cause a fast travelling motor vehicle suddenly to veer sideways on a dry straight road?

Your answer is correct. A strong side wind or a burst tyre can both cause a vehicle to suddenly veer to the side, even on a dry and straight road. A sudden gust of wind can push the car sideways, especially at high speed. Similarly, if a tyre bursts, the vehicle may swerve sharply toward the side of the burst. Sudden headwind, however, does not cause the vehicle to veer sideways; it only slows the car down. Knowing these causes helps drivers respond quickly and safely if they experience sudden sideways movement while driving.