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Flash Cards

Problems and Solutions about distance and displacement are presented and updated useful for highschool and college students. Problem 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 to problem 1: (a) By definition of displacement, connect the initial (A) and final (D) points together. As shown, displacement is toward the negative of the y-axis and its magnitude is equal to th

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Definition of projectile motion: Any object that is thrown into the air with an angle $\theta$ is projectile and its motion called projectile motion. In other words, any motion in two dimensions and only under the effect of gravitational force is called projectile motion.  Formula for Projectile Motion: The following are the complete projectile motion equations in vertical and horizontal directions. In horizontal direction: \begin{align*} \text{Displacement}&:\,\Delta x=\underbrace{\left(v_0 \cos \theta\right)}_{v_{0x}}t\\ \text{Velocity}&:\, v_x=v_0 \cos \theta \end{align*} In vertical direction: \begin{align*} \text{Displacement}&:\, \Delta y=\frac 12

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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

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