Explanation:

When the v-t graph of a particle is not a straight line, it means that the particle is experiencing a variable acceleration. This can be explained by the following points:

1. Definition of acceleration: Acceleration is defined as the rate of change of velocity of an object with respect to time. In other words, it is the change in velocity of an object per unit time.

2. Non-linear v-t graph: When the v-t graph of a particle is not a straight line, it means that the velocity of the particle is changing at a non-uniform rate. This implies that the acceleration of the particle is also changing.

3. Different types of variable acceleration: The acceleration of a particle can change in different ways. For example:

- Increasing acceleration: The particle can be accelerating at an increasing rate, which means that its velocity is increasing at an increasing rate. This is represented by a curved v-t graph that is concave upward.

- Decreasing acceleration: The particle can be decelerating, which means that its velocity is decreasing. This is represented by a curved v-t graph that is concave downward.

- Changing direction: The particle can be changing direction, which means that its velocity is changing from positive to negative or from negative to positive. This is represented by a v-t graph that has a sharp turn or a cusp.

Conclusion:

In conclusion, when the v-t graph of a particle is not a straight line, it implies that the particle is experiencing a variable acceleration. This can be due to different factors, such as increasing or decreasing acceleration or changing direction.