The graph bet ween kinetic energy (E) and speed (v) of the body is correctly shown by

Options

A.
B.
C.
D.

Answer

To determine the correct graph between kinetic energy (E) and speed (v) of a body, we start by recalling the formula for kinetic energy:

1. **Write the formula for kinetic energy:**
\[ E = \frac{1}{2} mv^2 \]
where \( E \) is the kinetic energy, \( m \) is the mass of the body, and \( v \) is its speed.

2. **Identify the relationship between kinetic energy and speed:**
In the formula, we can see that kinetic energy \( E \) is proportional to the square of the speed \( v \). This means:
\[ E \propto v^2 \]

3. **Rearranging the equation:**
We can express this relationship as:
\[ E = \frac{1}{2} m v^2 \]
Here, \( \frac{1}{2} m \) is a constant (let's denote it as \( p \)), so we can rewrite it as:
\[ E = p v^2 \]

4. **Identify the type of graph:**
The equation \( E = p v^2 \) is in the form of \( y = ax^2 \), where \( y \) is the kinetic energy \( E \), \( x \) is the speed \( v \), and \( a \) is a positive constant \( p \). This indicates that the graph of kinetic energy against speed will be a quadratic function.

5. **Determine the shape of the graph:**
Since the coefficient of \( v^2 \) is positive, the graph will be an upward-opening parabola.

6. **Select the correct option:**
Based on the analysis, the graph between kinetic energy and speed will be an upward parabola. Therefore, we look for the option that represents an upward parabola.

7. **Conclusion:**
The correct option that represents the graph between kinetic energy (E) and speed (v) is option 1, which is an upward parabola.