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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.)
This example neglects the effects of tire sliding, suspension dipping, real deflection of all ideally rigid mechanisms, etc. Another example of significant jerk, analogous to the first example, is the cutting of a rope with a particle on its end. Assume the particle is oscillating in a circular path with non-zero centripetal acceleration.
Position vs. time graph In the study of 1-dimensional kinematics , position vs. time graphs (called x-t graphs for short) provide a useful means to describe motion. Kinematic features besides the object's position are visible by the slope and shape of the lines. [ 1 ]
Example of a velocity vs. time graph, and the relationship between velocity v on the y-axis, acceleration a (the three green tangent lines represent the values for acceleration at different points along the curve) and displacement s (the yellow area under the curve.)
In contrast to an average velocity, referring to the overall motion in a finite time interval, the instantaneous velocity of an object describes the state of motion at a specific point in time. It is defined by letting the length of the time interval Δ t {\displaystyle \Delta t} tend to zero, that is, the velocity is the time derivative of the ...
Date/Time Thumbnail Dimensions User Comment; current: 01:22, 25 February 2007: 496 × 504 (111 KB) Stannered {{Information |Description=Example of a en:velocity vs. time graph, and the relationship between velocity v, en:displacement s, and en:acceleration a. Traced in en:Inkscape from an original drawn in en:Microsoft Paint. |Source=[[:
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.
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