May I recite Tehillim while jogging or performing other kinds of physical exercise?
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Offhand, the only issues I can think of are (a) if there's excrement or something else smelly nearby, or (b) if there are immodestly dressed women in your field of vision.
So if you're jogging in an area where the dog owners are careful to clean up after their pets, and there aren't any women also out jogging in shorts or sports bras, then I would think it should be fine (and indeed even a good thing, "purifying the air" with words of Torah). CYLOR, as usual.
"May I" or "Should I"? I think Alex covered all the Halachically problematic issues, but what about whether or not it's proper? It might not be, since you are almost definitely not going to be able to concentrate on the Tehillim you recite while jogging. On the other hand, if you are concentrating well on the Tehillim, you may pose a danger to yourself or others on the jogging path because you may not be concentrating on your exercise.
I would also further caution you that after a few minutes you might find it hard maintain the optimal pace for a good workout or catch your breath (exercising while speaking generally is difficult if you take the exercise seriously enough).