Answer:
(a) i) The distance travelled by the cycle in half round is approximately 65.97 m
ii) The displacement is 42 m
(b) (i) The distance travelled in one round is approximately 131.95 m
(ii) The displacement of the cycle in one round is 0
Explanation:
The diameter of the track through which the cycle travels, D = 42 m
(a) i) Half round is the motion of half the length of the circular path
The distance travelled by the cycle in half round = The length of half the circular track = (1/2) × π × D
∴ The distance travelled by the cycle in half round = (1/2) × π × 42 m = 21·π m ≈ 65.97 m
ii) The displacement half round = The change in the location of the cycle = The difference between the start and stop locations of the cycle on a straight line after half round
The angle at the center of the circular path the cycle turns in half round  = 180°
Therefore, the path between the start and stop location of the cycle in half round = The diameter of the circular track
The displacement of the cycle in half round = The diameter of the circular track = 42 m
(b) (i) The distance travelled in one round = The perimeter of the circular track = π·D
∴ The distance travelled in one round = π × 42 m ≈ 131.95 m
(ii) The displacement of the cycle in one round = The change in the location of the cycle
The start and stop location of the cycle after moving one round is the same, therefore, there is no change in the location of the cycle.
Therefore we have;
The displacement of the cycle in one round = 0 (no change in location of the cycle)
