What is the effect of changing the initial position on position time and velocity time graph?

Answer 1

Changing the initial position on a position vs time graph has no effect on the velocity vs time graph. Velocity is the derivative of position. This means velocity only depends on the rate of change (slope) of position. Changing the initial position of an object has no effect on the slope. Mathematically, this is equivalent to adding a constant to a function. Since the derivative of a constant is always 0, a change in initial position has no impact on the derivative. Here is an example.

Say we have the position functions x(t)= 4+9t and y(t)= 27+9t.

then the velocity function of x would be x'(t)=v(t)= 9

And the velocity function of y would be Y'(t)=v(t)= 9

Answer 2

If the initial position is changed, then

-- The whole line or curve on the distance/time graph moves some distance to the right or left.

-- Nothing changes on the speed/time graph.

(I don't call them "position" and "velocity" graphs, because direction has to be

part of position and velocity, and graphs don't tell you anything about direction,

only magnitude.)

Answer 3

The position-time graph will simply be translated in the Cartesian plane. If the initial position has been moved u units to the right and v units up then the graph will be moved u units to the left and w units down. So not much change.

However, the velocity-time graph will be altered out of all recognition. This is because the velocity-time graph is concerned only with movement in the direction from the initial position. Any component of motion in a direction at right angles to the initial point is completely ignored.

For example, consider a body which is moving at constant velocity around the initial position. At no time is the object moving towards or away from the initial point and so the V-T graph will be the same as the time axis. Next move the initial point to a point on the circumference of the circle. Now, for half the time the object is moving towards the "reference" point so that the graph is below the time axis, and for the other half it is moving away and so is above the axis. It fact, it will be a sinusoidal curve - nothing at all like the straight line with the old initial point.