is there a equation to find position in physics?

Answer 1

Position of a particle is given by s = ut + 0.5 at^2 where

s is the distance from an arbitrary reference point, u the initial velocity if any at that point and a the accleration if any of the particle. If a is zero, the equation becomes s = ut and is represented by a straight line of the form y = mx where the time is along the x axis and the position is along the y - axis.

Answer 2

Yes.

Let
v(0) = initial velocity, in other words velocity when t=0
t = elapsed time
a = acceleration
x = position (displacement from original position)

Assuming that acceleration is constant in both amount and direction, then position at time t is
x = v(0)*t + 1/2 a(t^2)

watch your units and dimensions; keep them consistent.
e.g. if a = -10 m/sec^2
make sure v is expressed in m/sec
and time is expressed in sec
so that x will be in m (=meters)

also, realize that x, v and a are all vectors (a vector has a quantity and also a direction).
assuming your problem is in at most two dimensions,
you can treat the problem as two separate problems,
and solve for x and y displacement separately.

special cases:
if you're launching a projectile straight up, then you're concerned only with "y-axis" displacement/position. "X-axis" displacement/position is always zero. and your acceleration (on earth's surface e.g. is -10m/sec^2, approx).

if you're launching horizontally, you need to know your initial y-axis position (height), and then determine the t (seconds) at which the projectile will hit the ground.

If you're launching at an angle, then you use trigonometry to determine the y and x components of the initial velocity vector, and take it from there. e.g launch at theta degrees relative to horizontal; then

v(0) y component = v(0) * sin(theta)
v(0) x component = v(0) * cos(theta)

hope this helps

Answer 3

Position in space-time is denoted as p(x,y,z,t) when given in Cartesian coordinates. We frequently call x, y, and z width, length, and height. t of course is time. We call our universe a 4 dimensional one because x, y, z, and t are four dimensions needed to specify a position in it. Time is needed when x, y, and/or z are moving for example. When they move over time, that's called velocity.

It can be shown that, for a given time, the distance R from the origin p(0,0,0,t) to p(X,Y,Z,t) is R = sqrt(X^2 + Y^2 + Z^2). This latter is a very popular equation used in physics and other scientific disciplines to define position. Velocity for this equation is shown as dR/dt = d[sqrt(X^2 + Y^2 + Z^2)]/dt. The d*/dt symbols mean "change in * divided by change in time." These are used in calculus, a mathematics of motion and other changes.

There are other coordinate systems, like sphereical, where position is given as p(R,theta,phi,t). R is the same R as above, but theta and phi are angles that give where in space R is pointing. This system is useful when defining positions on balls or spheres. An example is when giving a position on Earth's surface (at radius R) in latitude and longitude, both these latter dimensions are angles.

In fact, there is a branch of vectors, called curvilinear coordinates, that can be used to define poistion in just about any space-time coordinate system you'd like to use. We choose the coordinate system that makes finding the solution to our initial equations easier.