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Intro Definitions Equations 1-dimensional motion with constant acceleration If all objects either remained at rest or moved at constant speeds in straight lines, the world as you know it could not exist. Objects move in all manner of ways, some quite complex. Objects that do not remain at rest or move at constant speeds in straight lines are experiencing accelerated motion. A major part of this first lab examines the relationship between motion in a straight line, also called 1-dimensional motion, and the graphical representation of that motion. Consider these quantities of motion: distance traveled, displacement, speed, velocity, and acceleration. Can you write down the definition for each of these quantities? What is the difference between speed and velocity? How about distance traveled and displacement? How are graphs used to show these quantities? For motion of an object during a given time interval, Displacement is the resulting change of position during the interval. Distance is the length of the path the object travels during the interval. Average velocity is the change of displacement per unit time during the interval. Speed is the distance the object travels per unit time during the interval. Average acceleration is the change of velocity per unit time during the interval. Displacement, velocity, and acceleration are all vector quantities: these are described in terms of both a magnitude and a direction - direction will become very important when we discuss motion in more than 1 dimension. Speed and distance are scalar quantities: these are described in terms of magnitude (but not direction). Motion is best described and measured relative to a frame of reference and a clock. A frame of reference is a coordinate system. Suppose an object moves along a straight line. Using the straight line as the x-axis of a coordinate system, we take these readings: at time t = 0, the object is at position X and travels with velocity vo; at time t, the object is at position x and travels with velocity v. Equations describing the motion are expressed in terms of the coordinate and clock readings. For arbitrary motion along a straight line, these equations apply: displacement: Ax = x-xo time interval: At = t-t = t Ax average velocity: v= At x-Xo t average acceleration: a = At V-Vo t For motion with constant acceleration, a, these equations also apply: x = x + vot + at v = v + 2a(x-x) Vo V = V + at (v + Vo) Ax = vt = t 2