Q: What does the y intercept on a position vs time graph tell us?

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If the graph of position vs. time is curved upward to the right, then speed (velocity) is increasing. Refer to the related link for more information.

The Average Velocity on a position time graph or a velocity time graph.

-- If the position/time graph is a straight line, then the speed is constant, and the slope of the line is the average speed, as well as the instantaneous speed at any moment. -- If the position/time graph is not a straight line, then the average speed between two moments in time is the slope of a straight line drawn between those two points on the graph.

Yes. Free fall can be graphed on a position-time graph and a velocity-time graph. Refer to the related link below for examples.

Assuming position is on the y axis and time is on the x axis, a positive slope means the position has increased over time.

Related questions

Initial position is got by the y-intercept

In such graphs the x-axis is usually (but not always) the time axis. The x-intercept represents the time(s) at which your position is at the starting point - either for the first time or later.

Distance covered at a given time.

A position-time graph, is one in which position is plotted on the y-axis and the time is on the x-axis. A position-time graph is similar to a distance-time graph, but direction of motion in the y-axis.

Why don't you relax and tell me something about the situation.

The velocity of the object at time = 0

If the position is graphed vs time, then the slope (rate of change of position with respect to time) will be the same (parallel).

The velocity position time graph is rightward. This can change at anytime.

The starting speed.

If time is the x-axis as expected then the x-intercept would be zero movement of the velocity.

No. Slope of position/time graph is speed, or magnitude of velocity.Slope of speed/time graph is magnitude of acceleration.

The area of a position-time graph does not have a meaning. However, the area under a velocity-time graph is the displacement. Refer to the related link below for an illustration.