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**Motion in Two and Three Dimensions**

Position and Displacement Velocity and Acceleration Projectile or Ballistic Motion Range Equation Uniform Circular Motion Relative Motion pps by C Gliniewicz

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**The displacement is the change in the position vector. **

The position vector is a vector which points from the origin to the location of the particle. The displacement is the change in the position vector. Average and instantaneous velocity can be determined from the displacement. The scalar components of the velocity are the derivatives of each coefficient. Average and instantaneous acceleration can be determined in the same way from the velocity. pps by C Gliniewicz

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**The path of the projectile can be shown by equations for the position.**

A projectile is an object which is projected or launched in a vertical plane with some initial velocity but its acceleration is always vertical and downward due to gravity. The horizontal and vertical motions are independent of one another. Neither motion affects the other. The horizontal motion remains constant. The vertical motion is always accelerating downward. The path of the projectile can be shown by equations for the position. The maximum horizontal range is reached when the launch angle is 45 degrees when the air resistance is zero. In reality air friction slows the object and it travels a shorter distance horizontally and vertically. pps by C Gliniewicz

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A particle moving in uniform circular motion travels at a constant speed, but the velocity is changing because the direction is changing. Therefore the object is accelerating and the acceleration is radially inward toward the center. This is centripetal acceleration. When two frames of reference A and B are moving relative to each other at constant velocity, the velocity of a particle, p, as measured by an observer in frame A differs from an observer in frame B by the velocity difference of the two frames of reference. The accelerations observed by the two observers is the same since their velocities are constant. pps by C Gliniewicz

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