Final answer:
The valid velocities are 46 m/s, 67 km/hr west, and 0 m/s north.
Step-by-step explanation:
In physics, it's crucial to use consistent units and include directional information when expressing velocities. Let's delve into the explanation for the correct choices:
a. 46 m/s: This option provides a velocity in meters per second, which is the standard SI unit for velocity. The direction is not explicitly mentioned, but the absence of a specified direction doesn't invalidate it as a velocity.
c. 0 m/s north: Even though the magnitude is zero, indicating no speed, it still qualifies as a velocity since it includes direction (north). Direction is a key component when describing velocity, even when the magnitude is zero.
e. 67 km/hr west: While the unit is not in the standard SI form (meters per second), it still represents a valid velocity. The inclusion of direction (west) is crucial for defining velocity accurately.
Options b, d, and f are excluded due to issues with units or missing directional information. Consistency in units and the inclusion of direction are vital in accurately describing velocities in physics.