Question

E Describe the meaning of a line crossing the x-axis in a
velocity-time graph.

Answer 1

A line crossing the x-axis on a velocity-time graph signifies that the object is momentarily at rest, with zero velocity at that point. A horizontal line indicates constant velocity (no acceleration), while a sloped line shows variable velocity, indicating acceleration. The area under the curve represents the object's displacement.

Step-by-step explanation:

A line crossing the x-axis in a velocity-time graph represents a moment when the object is momentarily at rest, meaning its velocity is zero. This occurs at the exact point where the line touches the x-axis. For example, a rock thrown into the air will come to a stop momentarily at the peak of its flight before beginning to fall back to Earth. In such a case, the graph would show a line crossing the x-axis at that peak moment.

Moreover, the slope of a velocity-time graph indicates acceleration. A horizontal line on a velocity-time graph means that the object is moving with a constant velocity and, therefore, is not accelerating. On the other hand, a sloped line indicates that the object's velocity is changing, showing that it has acceleration. The steeper the slope, the greater the acceleration.

Answer 2

A line crossing the x-axis in a velocity-time graph means that the moving object has changed its direction.

Step-by-step explanation:

Velocity-Time graph:

A velocity-time graph is a two dimensional graph with velocity at its y-axis and time at its x-axis. At any point, value of y represents the velocity and value of x represents the time. The slope of the graph gives us the acceleration or deceleration of the moving object.

In a velocity-time graph:

- A straight line represents constant velocity.

- A diagonal line means that the velocity of a body is changing.

*Referring to the figure attached with the answer*

The velocity of the moving object increases at a constant rate for the first 10 minutes. Then the velocity is 60 m/min for the next 5 minutes. After that the velocity is decreasing. Till 30th minute when the velocity is at 0 m/min.

What happens here?

Velocity is a vector quantity. It has some direction. In a velocity-time graph, we are only concerned with two directions of velocity:

- Forward direction

- Backward direction

So, the object stops at 30th minute and starts moving in the reverse direction after that with an increasing velocity. The point where the line cuts the x-axis is basically the point where the object starts moving in the reverse direction.