Question

A person travels on a semi-circular track of radius $50\text{m}$ during a morning walk. If he starts from one end of the track and reaches the other end. Calculate the distance traveled and the magnitude of displacement of the person.

• A. Distance $=157.4\text{m}$ and Displacement $=100\text{m}$
• B. Distance $=75.4\text{m}$ and Displacement $=50\text{m}$
• C. Distance $=314.8\text{m}$ and Displacement $=200\text{m}$
• D. Distance $=174\text{m}$ and Displacement $=20\text{m}$

Answer 1

Answer: (A)

Step 1, Given data

The radius of the track = 50 m

Track is semi-circular

Step 2, Finding the distance and displacement
Let the person starts moving from $A$ and reaches at $B$ via $C$.

Then, the distance traveled by the person $=$ Length of the semi-circular track = $\pi r=\frac{22}{7}\times 50$ $=157.14\text{m}$
The displacement is equal to the shortest distance between the initial and final position si it will be the diameter of the semi-circular track joining $A$ to $B$ via $O$.
$=2r=2\times 50\text{m}=100\text{m}$.