Step 1: Understand the function of an odometer.
An odometer is an instrument used to measure the distance traveled by a vehicle. It typically records the total cumulative distance from the time the vehicle was manufactured or reset.
Step 2: Differentiate from other measurements.
Speed is measured by a speedometer, which indicates how fast the vehicle is moving at a particular instant.
Acceleration is the rate of change of velocity, which is not directly measured by a standard odometer.
Velocity is speed in a given direction, also not directly measured by an odometer.
Step 3: Conclude the primary measurement of an odometer.
The primary and sole function of an odometer is to measure the total distance covered by the vehicle.
Step 4: Compare the conclusion with the given options.
The odometer of a vehicle measures distance.
$$(2) Distance$$