# Flash Cards

kinemtic

## Simplest examples of displacement and distance (quick review)

Displacement: is a vector quantity that connects the initial and final positions of a moving object by the shortest line.  Distance: is a scalar quantity that measures the lengths of the total path covered by a moving object. Example 1:  An object moves from point A to B, C, and D finally along a rectangle.  (a) Find the magnitude and direction of the displacement vector of the object? (b) Find the distance traveled by that object? (c) Suppose the object returns to the point A, its initial position. Now, Find the displacement and distance? Solution: (a) By definition of displacement, connect the initial (A) and final (D) points together. As shown, displacement is

Average velocity: is defined as the displacement vector divided by the total time elapsed from start to finish or in math language is defined by formula: $v_{av-x}=\frac{\Delta x}{\Delta t}=\frac{x_f-x_i}{t_f-t_i}$ Instantaneous velocity: is the limit of the average velocity as $\Delta t$ approaches zero. In one dimension, say $x$, is defined by formula $v_x=\lim_{\Delta t\to 0} \frac{\Delta x}{\Delta t}=\frac{dx}{dt}$ Instantaneous acceleration: is the limit of the average acceleration as $\Delta t$ approaches zero. In one dimension, say $x$, is defined by the followin formula $a_x=\lim_{\Delta t\to 0}\frac{\Delta v_x}{\Delta t}=\frac{dv_x}{dt}=\frac{d^2 x}{dt^2}$ \$d^{2}x/dt^2