A body is thrown vertically upwards which graph represents variation of velocity w.r.t time

Options

A.
B.
C.
D.

Answer

To solve the problem of determining which graph represents the variation of velocity with respect to time for a body thrown vertically upwards, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Motion**: When a body is thrown vertically upward, it initially moves upward with a certain velocity (let's call it \( u \)). As it rises, it experiences a downward acceleration due to gravity (\( g \)).

2. **Write the Equation of Motion**: The velocity \( v \) of the body at any time \( t \) can be expressed using the equation of motion:
\[ v = u - gt \]
Here, \( u \) is the initial velocity, \( g \) is the acceleration due to gravity (which is taken as positive but acts in the negative direction), and \( t \) is the time elapsed.

3. **Analyze the Equation**: The equation \( v = u - gt \) indicates that the velocity decreases linearly over time due to the negative acceleration (gravity). When \( t = 0 \), the velocity is \( u \). As time increases, the term \( -gt \) becomes larger, causing the velocity \( v \) to decrease.

4. **Determine the Velocity at Maximum Height**: The body will continue to rise until its velocity becomes zero. Setting \( v = 0 \) gives:
\[ 0 = u - gt \implies t = \frac{u}{g} \]
This is the time at which the body reaches its maximum height.

5. **Behavior After Maximum Height**: After reaching the maximum height, the velocity becomes negative as the body starts to fall back down. The velocity will continue to decrease in the negative direction as it falls back to the ground.

6. **Graph Characteristics**: The graph of velocity versus time will start at \( u \) (positive), decrease linearly to 0 (at the maximum height), and then continue to decrease into negative values as the body falls back down. This results in a straight line that slopes downwards.

7. **Select the Correct Graph**: From the options provided, we need to identify the graph that starts at a positive value (initial velocity \( u \)), decreases linearly to zero, and then continues into the negative region.

### Conclusion:
The correct graph representing the variation of velocity with respect to time for a body thrown vertically upwards is the one that starts from a positive value, decreases linearly to zero, and then goes into the negative region.