Question

What measurements or observations tells you that a car is accelerating

Answer 1

You need to observe the car at two different times.

-- The first time: 
You write down the car's speed, and the direction it's pointing.

-- The second time:
You write down the car's speed and the direction it's pointing, again.

You take the data back to your lab to analyze it.

-- You compare the first and second speed. If they're different,
then the car had acceleration during the time between the two
observations.

-- You compare the first and second direction.  If those are different,
even if the speeds are the same, then the car had acceleration during
the time between the two observations.

(Remember, "acceleration" doesn't mean "speeding up". 
It means any change in speed or direction of motion.)

Answer 2

Frame of reference. It uses the second law of motion to determine whether it is moving or not...