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Acceleration on a position vs. time graph can be obtained, by having the initial position and velocity of a moving object. In this article, we want to show you how to find constant acceleration from a position-time graph with some solved problems. You can skip this introduction and refer to problems 6 and 7.  Types of Motion: An object can move at a constant speed or have a changing velocity. Suppose you are driving a car at a constant speed of $100\,{\rm km/h}$ along a straight line. What does mean by $100\,{\rm km/h}$?  The speed of $100\,{\rm km/h}$ indicates that you drive the first 100 km in the first hour, the next 100 km during the second hour, an

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Problems and Solutions about distance and displacement are presented and updated useful for high school and college students. In the following, displacement is computed for simple cases, 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 point A, its initial position. Now, Find the displacement and distance?   Solution (1): (a) By definition of displacement, connect the initial (A) and final (D) points together. As shown, displacement is toward the n

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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 all projectile motion equations in vertical and horizontal directions. In horizontal direction: \[\begin{aligned} \text{Displacement}&:\,\Delta x=\underbrace{\left(v_0 \cos \theta\right)}_{v_{0x}}t\\ \text{Velocity}&:\, v_x=v_0 \cos \theta \end{aligned}\] In vertical direction: \[\begin{aligned} \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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