Force Acting on the Block:
The force \( F \) acting on the block increases linearly with time \( t \).
We can write:
\[ F = kt \] where \( k \) is a constant of proportionality.
Using Newton's Second Law to Find Acceleration:
According to Newton's second law, the acceleration \( a \) of the block is given by:
\[ F = ma \]
Substituting \( F = kt \):
\[ ma = kt \implies a = \frac{kt}{m} \]
where \( m \) is the mass of the block.
Relation Between Acceleration and Time:
From the equation \( a = \frac{kt}{m} \), we see that the acceleration \( a \) is directly proportional to time \( t \).
This means that as time \( t \) increases, the acceleration \( a \) also increases linearly.
Conclusion:
The correct graph representing the acceleration of the block with time is a straight line passing through the origin, as shown in Option (2).
Match the following List-I with List-II and choose the correct option: List-I (Compounds) | List-II (Shape and Hybridisation) (A) PF\(_{3}\) (I) Tetrahedral and sp\(^3\) (B) SF\(_{6}\) (III) Octahedral and sp\(^3\)d\(^2\) (C) Ni(CO)\(_{4}\) (I) Tetrahedral and sp\(^3\) (D) [PtCl\(_{4}\)]\(^{2-}\) (II) Square planar and dsp\(^2\)
Let A be a 3 × 3 matrix such that \(\text{det}(A) = 5\). If \(\text{det}(3 \, \text{adj}(2A)) = 2^{\alpha \cdot 3^{\beta} \cdot 5^{\gamma}}\), then \( (\alpha + \beta + \gamma) \) is equal to: