El certificado médico es un requisito para la carrera del domingo.

In Spanish, it is very common to use the definite article where English might omit it.
So el certificado médico means the medical certificate.

Here, the article makes the noun phrase sound complete and natural. In many contexts, Spanish prefers:

• El certificado médico es obligatorio.
• La entrada cuesta diez euros.
• El agua está fría.

Even if English might say medical certificate required, Spanish usually wants the article in a full sentence.

Because in Spanish, most descriptive adjectives normally come after the noun.

So:

• certificado médico = medical certificate
• coche rojo = red car
• casa grande = big house

This is the normal order. Putting the adjective before the noun is sometimes possible with some adjectives, but it often changes the tone or meaning. With médico, the standard order is definitely certificado médico.

Es is the third person singular of ser.

The subject is El certificado médico, which is singular, so the verb must also be singular:

• El certificado médico es...
• not son

Ser is used here because the sentence identifies something as a category or characteristic:

• Es un requisito.

That means the certificate is a requirement.

After ser, Spanish often uses an article when classifying something.

So:

• Es un requisito = It is a requirement
• Es una buena idea = It is a good idea

Without un, Es requisito is possible in some contexts, but it sounds more abstract, formal, or less natural in everyday speech.
For a learner, es un requisito is the safest and most natural choice.

Here, para means something like for or in order for.

So:

• un requisito para la carrera = a requirement for the race

It shows the purpose or target of the requirement.

Compare:

• Necesito un documento para el trabajo. = I need a document for work.
• Esto es para ti. = This is for you.

In this sentence, the medical certificate is required for participating in / for the purposes of the Sunday race.

No. Carrera has several meanings, and this is a very common source of confusion for English speakers.

It can mean:

• race
• degree course / university course of study
• career / profession in some contexts

In this sentence, la carrera del domingo means the race on Sunday, not career.

In Spain, carrera is very commonly used for a running race or organized race event.

Del is the contraction of de + el.

So:

• del = de el

Because domingo here is treated as a noun with the article el, Spanish contracts them:

• la carrera del domingo
• not la carrera de el domingo

This is exactly like:

• el libro del profesor = the teacher’s book
• la puerta del coche = the car door

In Spanish, days of the week often use the definite article:

• el domingo = Sunday / on Sunday
• los domingos = on Sundays / every Sunday

In la carrera del domingo, it means the race on Sunday or the Sunday race.

This is very natural in Spanish. English often leaves out the article, but Spanish usually includes it.

It can correspond to both in English.

Spanish often uses de + article + noun where English might use either:

• an apostrophe construction: Sunday’s race
• or a prepositional phrase: the race on Sunday

So la carrera del domingo is best understood as the race taking place on Sunday.

Yes, but it changes the structure and the emphasis.

• El certificado médico es un requisito para la carrera del domingo.
  = The certificate is a requirement for the Sunday race / the race on Sunday.

• El certificado médico es un requisito para correr el domingo.
  = The certificate is a requirement to run on Sunday.

The original sentence focuses on the event (la carrera).
The alternative focuses more on the action (correr).

Both can be correct depending on what you want to emphasize.

It most naturally refers to a specific race, because of:

• la carrera = the race
• del domingo = of Sunday / on Sunday

So it sounds like there is a particular race happening on Sunday, and the medical certificate is required for that event.

If you wanted a more general statement, you might say something like:

• Un certificado médico es un requisito para participar en estas carreras.

Yes, depending on context.

Requisito usually means:

• requirement
• sometimes prerequisite
• sometimes condition

In this sentence, requirement is the most natural translation.
Prerequisite is possible, but it sounds a little more formal in English.

A little, yes, but the original order is the most natural and neutral.

Standard order:

• El certificado médico es un requisito para la carrera del domingo.

You could also say:

• Para la carrera del domingo, el certificado médico es un requisito.

That version puts emphasis on for the Sunday race.

Spanish allows more flexibility than English, but not every possible order sounds equally natural. The original sentence is clear, neutral, and standard.

A Spaniard might say the original sentence exactly as it is, because it is already natural. But in everyday speech, you might also hear:

• Hace falta un certificado médico para la carrera del domingo.
• Piden certificado médico para la carrera del domingo.

These alternatives are a bit more conversational:

• Hace falta... = ...is needed
• Piden... = They ask for / They require

The original sentence sounds slightly more formal or official, which fits well with words like certificado and requisito.