Search results
Results from the WOW.Com Content Network
In geometry, a position or position vector, also known as location vector or radius vector, is a Euclidean vector that represents a point P in space. Its length represents the distance in relation to an arbitrary reference origin O , and its direction represents the angular orientation with respect to given reference axes.
In geometry and mechanics, a displacement is a vector whose length is the shortest distance from the initial to the final position of a point P undergoing motion. [1] It quantifies both the distance and direction of the net or total motion along a straight line from the initial position to the final position of the point trajectory.
Since the velocity of the object is the derivative of the position graph, the area under the line in the velocity vs. time graph is the displacement of the object. (Velocity is on the y-axis and time on the x-axis. Multiplying the velocity by the time, the time cancels out, and only displacement remains.)
Trajectory of a particle with initial position vector r 0 and velocity v 0, subject to constant acceleration a, all three quantities in any direction, and the position r(t) and velocity v(t) after time t. The initial position, initial velocity, and acceleration vectors need not be collinear, and the equations of motion take an almost identical ...
Angular velocity: the angular velocity ω is the rate at which the angular position θ changes with respect to time t: = The angular velocity is represented in Figure 1 by a vector Ω pointing along the axis of rotation with magnitude ω and sense determined by the direction of rotation as given by the right-hand rule.
For constant velocity the position at time t will be = +, where x 0 is the position at time t = 0. Velocity is the time derivative of position. Its dimensions are length/time. Acceleration a of a point is vector which is the time derivative of velocity.
The instantaneous velocity equation comes from finding the limit as t approaches 0 of the average velocity. The instantaneous velocity shows the position function with respect to time. From the instantaneous velocity the instantaneous speed can be derived by getting the magnitude of the instantaneous velocity.
Figure 2: The velocity vectors at time t and time t + dt are moved from the orbit on the left to new positions where their tails coincide, on the right. Because the velocity is fixed in magnitude at v = r ω , the velocity vectors also sweep out a circular path at angular rate ω .