Are Elevated Pulse And Weakness In Legs Normal Post Cardio Exercises?

I am a 51 year old female, I recently started going to a gym. I weigh 135 lbs .trainer told me to start with cardio. After 2 minutes my heart rate is 140 after 6 minutes it goes up to 175+ my legs from knees down feel extremely fatigued. I know I am not in great shape but this seems to be extreme. Is this normal,?