$A$ circular cycle track has a circumference of $314 \ m$ with $AB$ as one of its diameters. $A$ cyclist travels from $A$ to $B$ along the circular path with a velocity of constant magnitude $15.7 \ m s^{-1}$. Find the:
$(a)$ distance moved by the cyclist.
$(b)$ displacement of the cyclist,if $AB$ represents the north-south direction.
$(c)$ the average velocity of the cyclist.

(N/A) Distance travelled by the cyclist $=$ length of the path $AB$ (semicircle) $=$ half the circumference of the circle.
$S = \frac{314}{2} = 157 \ m$.
$(b)$ The displacement of the cyclist is equal to the diameter $AB$ of the circle.
Since circumference $= 2 \pi r = 314 \ m$,therefore,
$r = \frac{\text{circumference}}{2 \pi} = \frac{314}{2 \times 3.14} = 50 \ m$.
Therefore,displacement of the cyclist $= 2 \times r = 2 \times 50 = 100 \ m$ towards south.
$(c)$ Average velocity is defined as the total displacement divided by the total time taken.
First,find the time taken: $\text{Time} = \frac{\text{Distance}}{\text{Speed}} = \frac{157 \ m}{15.7 \ m s^{-1}} = 10 \ s$.
Average velocity $= \frac{\text{Total Displacement}}{\text{Total Time}} = \frac{100 \ m}{10 \ s} = 10 \ m s^{-1}$ towards south.