После тренировки нам пора бы сделать заминку и немного потянуться.

Because после requires the genitive case.

• после тренировки = after the workout / after training
• base form: тренировка
• genitive singular: тренировки

So this is a very standard pattern:

• после урока = after the lesson
• после работы = after work
• после тренировки = after the workout

Пора is an impersonal word meaning it is time. The person who is concerned goes in the dative case, so:

• нам пора = it’s time for us
• literally: to us, it is time

That is why Russian uses нам, not мы.

Compare:

• мне пора идти = I have to go / it’s time for me to go
• тебе пора спать = it’s time for you to sleep
• нам пора сделать заминку = it’s time for us to do a cool-down

So the sentence has no normal subject like мы. It is an impersonal construction.

Here бы softens the statement and makes it sound less blunt, more like a suggestion or gentle conclusion.

• нам пора сделать заминку = it’s time for us to do a cool-down
• нам пора бы сделать заминку = we really should do a cool-down / it’d be about time to do a cool-down

In this sentence, бы does not create a full conditional meaning like would in English. Instead, it adds a nuance like:

• probably should
• really ought to
• it would be a good idea now

So the speaker is not just stating a fact; they are gently suggesting the next step.

Yes.

• После тренировки нам пора сделать заминку и немного потянуться.

This version is more direct and matter-of-fact: it’s time for us to do a cool-down and stretch a little.

With бы, the sentence sounds a bit softer and more conversational. Both are natural, but the nuance changes.

In sports and fitness, заминка means a cool-down: the light activity you do after training to help your body recover.

So:

• сделать заминку = do a cool-down

This is a common collocation in Russian fitness language.

Be careful: заминка can also mean a hitch, delay, or snag in other contexts. But here, because the sentence is about training, it clearly means cool-down.

Also, заминку is in the accusative case because it is the direct object of сделать:

• сделать что? → заминку

Because сделать is perfective, and the sentence is talking about a single complete action: doing a cool-down after a workout.

• сделать заминку = do a cool-down (as one completed action)
• делать заминку = be doing / do cool-downs in general, repeatedly, or as a process

After a specific workout, Russian naturally prefers the perfective:

• После тренировки надо сделать заминку.

It presents the cool-down as the next whole step to complete.

Here потянуться means to stretch oneself.

The -ся ending shows that the action refers back to the person doing it. So this is not stretch something; it is stretch your body / do some stretching.

In this context:

• немного потянуться = stretch a little / do a bit of stretching

This is a very natural way to talk about stretching after exercise.

Потянуться is the perfective form and often suggests a brief or single bout of stretching. That fits very well here, because the sentence is about what to do now, after one workout.

• потянуться = stretch a bit / do some stretching now
• тянуться = stretch, be stretching, or stretch regularly/in general

So немного потянуться sounds natural for do a little stretching after training.

Немного means a little / a bit. Here it modifies потянуться:

• немного потянуться = stretch a little

It makes the action sound light and moderate, which fits a post-workout cool-down very well.

Because пора can be followed by an infinitive, and here the speaker names two actions that are both appropriate now:

• сделать заминку
• и немного потянуться

So the structure is:

• нам пора бы + infinitive + и + infinitive

In English, this works like:

• it’s time for us to do a cool-down and stretch a little

Russian does not need to repeat anything extra between the two verbs.

The given word order is natural, but Russian word order is flexible.

Original:

• После тренировки нам пора бы сделать заминку и немного потянуться.

Possible variations:

• Нам после тренировки пора бы сделать заминку и немного потянуться.
• Нам пора бы после тренировки сделать заминку и немного потянуться.

These all mean roughly the same thing, but the emphasis shifts slightly.

The original version is very natural because it sets the time frame first:

• После тренировки → after the workout
• then what should happen next

Because После тренировки is just a normal prepositional phrase at the beginning of the sentence, not a separate clause.

So no comma is needed:

• После тренировки нам пора бы сделать заминку...

Russian, like English, usually does not put a comma after a simple introductory phrase of this type unless there is some special stylistic reason.