A wooden block is initially at rest on a smooth surface. Now a horizontal force is applied on the block which increases linearly with time. The acceleration- time (a - t) graph for the block would be
Let's analyze the problem step-by-step to find the acceleration-time graph for the wooden block.
Understanding the scenario: The block is initially at rest on a smooth surface, which means there is no friction acting on the block. A horizontal force is applied on the block, and this force increases linearly with time.
Key concept - Newton's Second Law: According to Newton's second law, the force acting on an object is equal to the mass of the object times its acceleration:
F = ma. Therefore, the acceleration can be expressed as:
a = \frac{F}{m}
Relation between force and time: The force is increasing linearly with time. If we represent the force as F(t) = kt, where k is a constant, then:
a = \frac{kt}{m} = \frac{k}{m}t
Acceleration as a function of time: The expression a = \frac{k}{m}t indicates that acceleration is directly proportional to time t. Therefore, the graph of acceleration vs. time will be a straight line with a positive slope.
Conclusion: Based on the analysis above, the acceleration vs. time graph is a straight line originating from the origin with a positive slope. This corresponds to the image provided in the correct answer option.
Thus, the correct acceleration-time graph for this scenario is the one represented by a straight line with a positive slope starting from the origin.
