I just bought a 99 4WD Automatic V6 Explorer. When going uphill, if I step on the gas and the engine downshifts, the truck veers to the right. This is very noticeable around 50 60 mph.
Also, some times when stopping, I feel a small lurch.
Are these symptoms of worn motor mounts?

 

Welcome to the forum!

Certainly check for worn engine mounts. The last time I experienced unusual torque steer that was also felt when hitting the brakes it was due to a broken unibody structure just behind the engine bay. Since your '99 would have a full frame, that's probably not the issue. However, if you're from an area where salt is used on the roads, or the truck is from one of those states, it's also worth checking.

There's of course also a chance that the acceleration pull and braking pull are unrelated, or are both due to sticking brake caliper or restricted brake hose. As a 1999 if the brake fluid has not been flushed regularly, the hoses could quite easily be degraded.

-Rod