Motor je při zkušební jízdě tichý.

Because motor is the subject of the sentence, so it is in the nominative singular.

• motor = nominative singular
• It is a masculine inanimate noun

In this sentence, motor is the thing being described as tichý.

Je is the 3rd person singular present tense of být = to be.

So the structure is:

• Motor = the engine
• je = is
• tichý = quiet

Literally: The engine is quiet during the test drive.

In standard Czech, you normally do need je in a sentence like this. Czech often omits subject pronouns, but not the verb to be here.

Because tichý is an adjective agreeing with motor.

Since motor is:

• masculine
• singular
• nominative

the adjective also has to be:

• masculine
• singular
• nominative

So:

• tichý motor = a quiet engine
• Motor je tichý = The engine is quiet

If the noun were different, the adjective would change:

• Auta jsou tichá = The cars are quiet
• Jízda je tichá = The ride is quiet

Při often means during, while, or in the course of.

So:

• při zkušební jízdě = during the test drive

It is a very natural preposition for talking about something happening in the course of an activity or event.

Other examples:

• při práci = during work / while working
• při jednání = during the meeting / negotiations
• při nehodě = during the accident / in the accident

Because the preposition při requires the locative case.

So jízda changes to jízdě:

• nominative: jízda
• locative: jízdě

And the adjective must match it:

• zkušební jízda = a test drive
• při zkušební jízdě = during the test drive

So the whole phrase is in the locative singular.

Because zkušební belongs to an adjective type that often has the same form in several cases.

Here it agrees with jízdě, but its form stays zkušební.

So even though the noun changes:

• jízda → jízdě

the adjective remains:

• zkušební → zkušební

This is normal for adjectives of this pattern, such as:

• jarní = spring
• poslední = last
• cizí = foreign

Yes. That is perfectly natural.

Czech word order is more flexible than English because case endings show grammatical roles. So these are both fine:

• Motor je při zkušební jízdě tichý.
• Při zkušební jízdě je motor tichý.

The difference is mainly focus:

• Motor je při zkušební jízdě tichý. → focuses a bit more on the engine
• Při zkušební jízdě je motor tichý. → starts with the situation/time context

Both mean essentially the same thing.

Not exactly.

• při zkušební jízdě = during the test drive
• na zkušební jízdě = on a test drive

So:

• Motor je při zkušební jízdě tichý focuses on what happens during that event.
• Jsme na zkušební jízdě means We are on a test drive.

Both can be natural, but they are used a little differently.

Yes. In Czech, motor is the normal word for an engine, especially in a vehicle context.

So in a sentence about a car, motor naturally means engine.

Examples:

• benzínový motor = petrol/gasoline engine
• dieselový motor = diesel engine
• vypnout motor = turn off the engine

So even though English distinguishes motor and engine more often, Czech motor is exactly what you would expect here.

A few things may stand out to an English speaker:

• při contains ř, the famous Czech sound
• í is a long vowel
• ě affects the consonant before it

A rough guide:

• při ≈ something like przhi but with the special Czech ř
• zkušební ≈ zkoo-sheb-nee
• jízdě ≈ yeez-dyeh

A more natural breakdown:

• Motor je při zkušební jízdě tichý
• roughly: MO-tor ye przhi zKOO-sheb-nee YEEZ-dyeh TI-khee

This is only an approximation, but it can help until you learn the exact Czech sounds.

It can do either, depending on context.

Most naturally, it means something like:

• The engine is quiet during a/the test drive
• In other words, when tested, the engine runs quietly

So it could describe:

1. a specific test drive
   for example, after inspecting a car

2. a general characteristic
   for example, in a product review or sales description

Czech does not have articles like a and the, so context tells you whether the meaning is specific or general.