Question

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 :

• A.
• B.
• C.
• D.

Answer 1

Answer: (B)

Answer 2

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).