Motion with Uniform Acceleration

Uniform acceleration refers to a situation where the rate of change of velocity of an object is constant over time. In other words, the object's velocity increases or decreases by the same amount in equal intervals of time.

v-t Graph

A velocity-time (v-t) graph represents the relationship between an object's velocity and time. It is a graphical representation that helps us understand how an object's velocity changes over time.

C Straight Line Inclined to the Time Axis

The correct answer to the given question is option C, which states that the v-t graph for motion with uniform acceleration is a straight line inclined to the time axis. Here's an explanation of why this is the case:

1. Uniform Acceleration
In motion with uniform acceleration, the velocity of an object changes at a constant rate. This means that the object's acceleration remains constant throughout the motion. For example, a car moving with a constant acceleration of 2 m/s^2 will increase its velocity by 2 m/s every second.

2. Varying Velocity
Since the velocity of the object is changing at a constant rate, the v-t graph will not be a straight horizontal line (option A) or a straight vertical line (option B). This is because the object's velocity is not remaining constant over time.

3. Inclined Straight Line
The v-t graph will be a straight line inclined to the time axis (option C). The slope of this line represents the acceleration of the object. The steeper the slope, the greater the acceleration, and vice versa. The line can be positively inclined (increasing velocity) or negatively inclined (decreasing velocity) depending on the direction of acceleration.

4. Example
For example, if a car is moving with a uniform acceleration of 2 m/s^2, its v-t graph will be a straight line inclined to the time axis. The slope of the line will be 2 m/s^2, indicating the constant acceleration. As time increases, the velocity of the car will increase linearly.

In conclusion, the v-t graph for motion with uniform acceleration is a straight line inclined to the time axis. This is because the velocity of the object is changing at a constant rate, represented by the slope of the graph.