A vehicle with a 160 mm diameter wheel turning at 100 rpm travels at a speed of approximatively 3.016 kilometers per hour.

$$v_{ (km.h^{-1}) } = \dfrac {3}{25}. \pi. r . N_{(rpm)}$$
$$v_{ (km.h^{-1}) } = \dfrac {3}{25} \times \pi \times 0.08 \times 100$$
$$v_{ (km.h^{-1}) } \approx 3.015928947446201 \text{ km/h}$$

To convert $100 \, \text{RPM}$ (Revolutions Per Minute) into kilometers per hour ( $\text{km/h}$ ) for wheels with a diameter of $160 \, \text{mm}$, follow these steps:

Step 1: Calculate the circumference of the wheel

The circumference of a wheel is given by:
$$\text{Circumference} = \pi \times \text{Diameter}.$$

For a wheel diameter of $160 \, \text{mm}$:
$$\text{Circumference} = \pi \times 160 \, \text{mm} = 502.65 \, \text{mm}.$$

Convert this to meters:
$$\text{Circumference} = 502.65 \, \text{mm} \div 1000 = 0.50265 \, \text{m}.$$

Step 2: Calculate the distance traveled in one minute

At $100 \, \text{RPM}$, the wheel completes $100$ revolutions in one minute. The distance traveled per minute is:
$$\text{Distance per minute} = 100 \times \text{Circumference}.$$

Substitute the circumference:
$$\text{Distance per minute} = 100 \times 0.50265 \, \text{m} = 50.265 \, \text{m}.$$

Step 3: Convert to meters per hour

There are $60 \, \text{minutes}$ in an hour, so the distance traveled per hour is:
$$\text{Distance per hour} = 50.265 \, \text{m/min} \times 60 \, \text{min/h} = 3015.9 \, \text{m/h}.$$

Convert meters per hour to kilometers per hour:
$$\text{Distance per hour} = 3015.9 \, \text{m/h} \div 1000 = 3.0159 \, \text{km/h}.$$

Final Answer:

At $100 \, \text{RPM}$ with $160 \, \text{mm}$ diameter wheels, the speed is approximately:
$$\boxed{3.016 \, \text{km/h}}.$$