Correct Option
The correct option isA curved line.
Explanation
Acceleration is defined as the rate of change of velocity with respect to time. Mathematically, instantaneous acceleration is the derivative of velocity ($a = \frac{dv}{dt}$). On a velocity-time graph, the slope (or gradient) of the curve at any specific point represents the acceleration of the object at that instant.
Option Analysis
- A straight line with constant slope. is incorrect: A straight line with a constant slope indicates that the rate of change of velocity is constant. This represents uniform acceleration.
- A curved line. is correct: A curved line on a velocity-time graph implies that the slope is changing continuously at every point. A changing slope indicates a changing rate of velocity, which represents non-uniform (variable) acceleration.
- A straight line parallel to the time axis. is incorrect: A straight line parallel to the time axis indicates that velocity remains constant over time. Since there is no change in velocity, the slope is zero, representing zero acceleration.
- A straight line parallel to the velocity axis. is incorrect: A straight line parallel to the velocity axis would imply an infinite slope, meaning a change in velocity occurs in zero time. This represents an infinite acceleration, which is physically impossible for a massive object.
Key Takeaway: In a velocity-time graph, the slope represents acceleration. A constant slope (straight line) denotes uniform acceleration, while a variable slope (curved line) denotes non-uniform acceleration.