Step 1: Understanding the Concept:
On a velocity-time (\(v-t\)) graph, the area enclosed by the graph and the time axis over a given interval represents the displacement of the particle during that interval.
If the graph is a straight line starting from the origin, it indicates uniform acceleration starting from rest.
Step 2: Key Formula or Approach:
Since the graph is a straight line from \((0,0)\) to \((10, 20)\), the shape formed under the graph is a triangle.
\[ \text{Displacement} = \text{Area of the Triangle} = \frac{1}{2} \times \text{Base} \times \text{Height} \]
Alternatively, we can use kinematic equations:
\[ s = \left( \frac{u + v}{2} \right) \times t \]
Step 3: Detailed Explanation:
1. Identify the dimensions of the triangle on the \(v-t\) plot:
- Base (time interval) = \( 10 - 0 = 10 \text{ s} \).
- Height (final velocity) = \( 20 - 0 = 20 \text{ m/s} \).
2. Calculate the area:
\[ \text{Displacement} = \frac{1}{2} \times 10 \text{ s} \times 20 \text{ m/s} \]
\[ \text{Displacement} = 5 \times 20 = 100 \text{ m} \]
3. Verification using kinematics:
- Initial velocity (\(u\)) = 0 m/s.
- Final velocity (\(v\)) = 20 m/s.
- Time (\(t\)) = 10 s.
- Average velocity = \( \frac{0 + 20}{2} = 10 \text{ m/s} \).
- Displacement = \( \text{Average Velocity} \times \text{Time} = 10 \times 10 = 100 \text{ m} \).
Step 4: Final Answer:
The total displacement in 10 seconds is 100 m.
This matches Option (B).