The velocity of a boedy increases for some time, then attains a constnat value and finally the velocity decreases until the body stops. What will be the shape of the velocity-time graph ?

Options

A. Straight line
B. Square
C. Circle
D. Trapezium

Answer

To solve the problem of determining the shape of the velocity-time graph based on the described motion of the body, we can break it down into three distinct phases as follows:

### Step-by-Step Solution:

1. **Phase 1: Velocity Increases**
- The body starts with an initial velocity and then its velocity increases over time. This means that as time progresses, the velocity is increasing. On a velocity-time graph, this will be represented as a straight line with a positive slope.
- **Graph Representation:** This part of the graph will be a straight line sloping upwards from the origin (or initial point).

2. **Phase 2: Constant Velocity**
- After the velocity has increased, the body then attains a constant velocity. This means that even as time continues to increase, the velocity remains unchanged.
- **Graph Representation:** This will be represented as a horizontal line parallel to the time axis on the graph, indicating that the velocity is constant over this period.

3. **Phase 3: Velocity Decreases to Stop**
- Finally, the velocity decreases until the body comes to a stop. This means that as time progresses, the velocity decreases until it reaches zero.
- **Graph Representation:** This will be represented as a straight line with a negative slope, sloping downwards until it intersects the time axis at the point where the velocity is zero.

4. **Combining the Phases**
- When we combine all three phases, we can visualize the entire velocity-time graph. The first phase is an upward sloping line, the second phase is a horizontal line, and the third phase is a downward sloping line that ends at the time axis.
- **Final Shape:** The overall shape of the graph resembles a trapezium (or trapezoid), where the first and last segments are sloped lines and the middle segment is a flat line.

### Conclusion:
The shape of the velocity-time graph for the described motion is a trapezium.

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