Corporate jet pilot reported the pilot flying descended too low on a visual approach and they received a terrain alert.

Narrative

This one report includes three separate parameter-deviations that happened in quick succession by the pilot flying. I was the assigned PIC (Pilot In Command)/PNF (Pilot Not Flying). We were on ZZZZZ X RNAV Arrival into ZZZ. We both are very experienced pilots with over 30000 hours between the two of us and around 10000 in the make and model of the airplane. We both are very conscientious too. Further; we know each other for about XX years and flown together extensively on and off. Yet; on this particular flight; the PF (Pilot Flying) crossed the ZZZZZ1 intersection about 200 feet high he then accelerated to 250 knots (assigned speed was 210 KIAS) while trying to keep up with the descend-via clearance. Right after that; while on Visual Approach to Runway XXR (backed up by RNAV/GPS XXR); he got too low on final. I kept announcing that we were low and slow; but his corrections were very minimal. We then got a 'too low; obstacle!' alert. We were in perfect VMC and did not see any obstacles; but; now he made a more assertive correction and returned to the glide path. The landing was uneventful.I could conclude with complex analysis of why and how; but; given our background together and my knowledge of this pilot's skills; I can tell you that he just had a bad day. He was very displeased with himself afterwards and tried to analyze what had happened. On my part; when I was telling him that we were low and slow and not getting the desired reaction; I should have changed my verbiage to something like 'push the throttles…'