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 determine the shape of the velocity-time graph for the given scenario, we can break down the motion of the body into three distinct phases:

### Step 1: Identify the phases of motion
1. **Acceleration Phase**: The velocity of the body increases over time.
2. **Constant Velocity Phase**: The body moves with a constant velocity.
3. **Deceleration Phase**: The velocity of the body decreases until it comes to a stop.

### Step 2: Draw the graph for each phase
1. **Acceleration Phase**:
- During this phase, as time increases, the velocity also increases. This can be represented as a straight line with a positive slope on the velocity-time graph.
- Let’s denote this line as segment A.

2. **Constant Velocity Phase**:
- In this phase, the velocity remains constant while time continues to increase. This is represented as a horizontal line on the graph.
- We can denote this line as segment B.

3. **Deceleration Phase**:
- In this phase, the velocity decreases until the body stops. As time increases, the velocity decreases, which can be represented as a straight line with a negative slope on the graph.
- We can denote this line as segment C.

### Step 3: Combine the segments
- The overall shape of the velocity-time graph will consist of three segments:
- Segment A (increasing velocity) is a straight line with a positive slope.
- Segment B (constant velocity) is a horizontal line.
- Segment C (decreasing velocity) is a straight line with a negative slope that ends at the time when the body stops (velocity = 0).

### Conclusion
- The resulting shape of the velocity-time graph will resemble a trapezium (or a trapezoidal shape) where:
- The left side represents the acceleration phase,
- The top horizontal part represents the constant velocity phase,
- The right side represents the deceleration phase.

### Final Answer
The shape of the velocity-time graph is trapezoidal.

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