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College and Engineering Physics Velocity and Speed The Particle Model Velocity Motion in One Dimension Uniform Motion Instantaneous Velocity Finding Position from Velocity 1 College and Engineering Physics Velocity and Speed The Particle Model A particle is an object that can be represented as a mass at a single point in space. This point is called the center of mass of the object. We will learn about this later. 2 The relationship between the force on the particle and the particle’s acceleration determine the path (trajectory) that the particle will follow. 1 Velocity College and Engineering Physics Velocity and Speed G v Velocity measures the motion of an object It consists of two parts … 1. The magnitude (speed) which is larger when the object is moving fast and smaller when the object is moving slow. The turtle has a smaller magnitude of velocity than the rabbit. 2. The direction tells you where the object is going. 3 The velocity of the airplanes has the same magnitude, but a different direction. College and Engineering Physics Velocity and Speed Horizontal Motion The x-component of most vectors (though not all) will be the component which is horizontal (lies along the plane of the earth). Variable Symbol (> 0) (< 0) Positive Negative y y Meaning of the Sign Determines a particle’s location Position x Velocity vx Determines the direction of the particle’s motion Acceleration ax Determines the direction of the change in a particle’s motion x x 4 2 College and Engineering Physics Velocity and Speed Vertical Motion The y-component of most vectors (though not all) will be the component which is vertical (points perpendicular to the plane of the earth). Variable Symbol (> 0) (< 0) Positive Negative y y Meaning of the Sign Determines a particle’s location Position y Velocity vy Determine the direction of the particle’s motion Acceleration ay Determines the direction of the change in a particle’s motion x x 5 College and Engineering Physics Velocity and Speed Average Velocity The direction and quantity of “motion” of a particle is given by its velocity. x The slope of this line is the x-component of the average velocity. ∆x ∆t t The average velocity of a particle (whether or not the motion is uniform) is given be a simple equation … G G ∆r vavg = ∆t 6 In words, we would say this equation tells us that “the average velocity of a particle is its displacement over the interval during which it moved”. 3 College and Engineering Physics Velocity and Speed Motion with Constant Velocity (Uniform Motion) If the position vs. time graph of a particle’s motion is a straight line, then the average velocity is the slope of this line and this component of the motion is uniform. x ∆x ∆t t Velocity is constant if it does not change. This means that the quantity (known as the magnitude) and the direction stay the same. 7 College and Engineering Physics Velocity and Speed G r vs. t Position vs. Time Graph To model the way a particle moves, we can use a graph of position vs. time. x y t y x 8 t 4 College and Engineering Physics Velocity and Speed G v vs. t Velocity vs. Time Graph Another way to model the motion of a particle is to graph velocity vs. time. Velocity is the derivative (slope) of the position over time. vx x t t 0s 1s 2s 3s 4s 5s 6s 7s 8s 0s 1s 2s 3s 4s 5s 6s 7s 8s 9 College and Engineering Physics Velocity and Speed G v vs. t Velocity vs. Time To determine where an object will be at a later time, we can use velocity vs. time curve. Time Vx (m/s) Velocity Position 4 3 2 1 t (s) 0 -1 -2 -3 -4 0 1 2 3 4 5 6 7 8 10 5 College and Engineering Physics Velocity and Speed G x vs. t Position vs. Time To determine where an object will be at a later time, we can use velocity vs. time curve. Time x (m) Velocity Position 8 6 4 2 t (s) 0 -2 -4 -6 -8 0 1 2 3 4 5 6 7 8 11 College and Engineering Physics Velocity and Speed Comparison To determine where an object will be at a later time, we can use velocity vs. time curve. Vx (m/s) x (m) 4 8 3 6 2 4 1 2 0 0 -1 -2 -2 -4 -3 -6 -4 12 -8 0 1 2 3 4 5 6 7 8 t (s) 0 1 2 3 4 5 6 7 8 x0 = 2 m x0 = −3 m 6