97 Camry vibration at speed and during braking

Hi all, I’m asking this on behalf of my dad who is too stubborn to address the problem.

We have a '97 Camry 4-cylinder with 93,000 miles on it that’s been vibrating quite noticeably during normal braking and after reaching about 70mph on the freeway. It tends to jerk in a pulsing sort of way (does that make sense?) while braking and, on the freeway, that same sensation is most noticeable when easing off the accelerator after a sprint. Can anyone shed light on this? All I know is that the tires are new.