With great difficulty since the question does not specify what aspect of the object's instantaneous. Speed, position, acceleration?
Besides obviously distance at any instant, on a connected, continuous distance-time graph, you can obtain instantaneous velocity and instantaneous acceleration.
To obtain the average velocity from a displacement-time graph, you can calculate the slope of the line connecting two points on the graph. Divide the change in displacement by the change in time. To obtain the instantaneous velocity, you need to find the slope of the tangent line at a specific point on the graph. Choose a point on the graph and draw a line tangent to the curve at that point. The slope of this tangent line will give you the instantaneous velocity at that specific point.
You can't, since the slope of the graph means average velocity and the area of the graph has no meaning. The only way to find instantaneous velocity from position-time gragh is by plugging the data into the kinematic equations to get the answer. Edit: Actually you can if you take the derivative of the equation of the curve it will give you the equation of the velocity curve
It is the gradient (slope) of the line.
graph it
A travel time graph can be used to find the distance from the epicenter of an earthquake.
this time is basically the instant when an object has a particular velocity(instantaneous velocity). so on the graph draw a line from the particular value of the velocity and then draw a vertical line on time axis to find the time for that velocity.
Just count the wavelengths distance.
No. What you've described is instantaneous acceleration. To lift the average speed from a graph, you need a graph of distance-time. Pick two points in time, and find the distance at both those times. The average speed over that time interval is (difference between the distances at the beginning and end) divided by (difference between the two times). If you're just going for the average, then it doesn't matter what happened during the interval, only the values at the end-points. The slope of the line tangent to the curve on your distance-time graph is the instantaneous speed at that point in time. We're saying "speed" in this discussion because there's actually no such thing as a graph of velocity. No simple thing anyway. Velocity is a vector, whose magnitude is speed and which includes a direction. It's easy to graph speed vs time, but not that easy to graph direction vs time. So all the graph shows is speed.
the distance from a epicenter to an earthquake :)
To find the average speed or rate of something.(:
That's correct, the instantaneous magnitudes are equal. Non-instantaneous values may not be equal. For example, to find average speed, between two points, you divide the actual path distance by the time, but for average velocity you divide the straight line distance, between the points, by the time. The straight line distance could be quite a bit shorter then the actual path distance (for curved motion) so you could get a big difference between those averages. When calculating "instantaneous" values, however, the difference between "actual path distance" and "straight line distance" becomes insignificant, because you are using distances for infintesimally small time intervals.