If you are asked to push an object so that the acceleration produced in it is now twice as before, then the force required will be

Options

A. twice as before
B. half as before
C. same as before
D. four times as before

Answer

To solve the problem, we need to understand the relationship between force, mass, and acceleration as described by Newton's second law of motion, which states:

\[ F = m \cdot a \]

Where:
- \( F \) is the force applied,
- \( m \) is the mass of the object,
- \( a \) is the acceleration produced.

### Step-by-Step Solution:

1. **Identify the Initial Conditions**:
- Let the initial acceleration of the object be \( a \).
- Let the mass of the object be \( m \).
- The initial force applied to produce this acceleration is \( F \).

\[ F = m \cdot a \]

2. **Determine the New Acceleration**:
- According to the problem, we want to double the acceleration. Therefore, the new acceleration \( a' \) will be:

\[ a' = 2a \]

3. **Calculate the New Force**:
- We need to find the new force \( F' \) required to achieve this new acceleration. Using Newton's second law again:

\[ F' = m \cdot a' \]

Substituting \( a' \) with \( 2a \):

\[ F' = m \cdot (2a) = 2 \cdot (m \cdot a) \]

4. **Relate the New Force to the Initial Force**:
- Since we know that \( F = m \cdot a \), we can substitute this into the equation for \( F' \):

\[ F' = 2F \]

5. **Conclusion**:
- Therefore, the force required to double the acceleration of the object is:

\[ F' = 2F \]

### Final Answer:
The force required will be **twice as before**.

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