A wooden block, initially at rest on the ground, is pushed by a force which increases linearly with time t. Which of the following curve best describes acceleration of the block with time :
The Correct Option is B
Solution and Explanation
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).
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