Two wheels roll towards each other with equal revolutions per second:\nTwo wheels with diameters 7 cm (smaller) and 14 cm (larger) start simultaneously from points X and Y that are 1980 cm apart, moving directly towards each other. Both wheels make the same number of revolutions per second and they meet after 10 seconds. Determine the linear speed of the smaller wheel in m/s (standardize units clearly).

Introduction / Context:
This problem connects rotational motion (revolutions per second) with linear speed along the ground. When two rolling wheels have equal revolutions per second, their linear speeds are proportional to their circumferences.

Given Data / Assumptions:

• Diameters: d_small = 7 cm, d_large = 14 cm.
• Separation = 1980 cm.
• They roll towards each other and meet in 10 s.
• Both have the same revs per second r.

Concept / Approach:
Linear speed v = (revs per second) * circumference. For each wheel, v = r * π * d. Closing speed = v_small + v_large.

Step-by-Step Solution:

Verification / Alternative check:
Ratio v_small : v_large = 7 : 14 = 1 : 2; v_small ≈ 0.66 m/s and v_large ≈ 1.32 m/s; sum ≈ 1.98 m/s ⇒ 1.98 m/s * 10 s = 19.8 m = 1980 cm, consistent.

Why Other Options Are Wrong:
22, 33, 44, 55 m/s are far too large for the given centimetre-scale wheels and distances.

Common Pitfalls:
Mixing units, using diameter instead of circumference directly, or forgetting that both advance toward each other.

Final Answer:
0.66 m/s.