College and Engineering Physics Velocity and Speed 1 TOC Motion in One Dimension Uniform Motion Instantaneous Velocity Finding Position from Velocity The Particle Model Velocity

College and Engineering Physics Velocity and Speed 2 TOC 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. The relationship between the force on the particle and the particle’s acceleration determine the path (trajectory) that the particle will follow. The Particle Model

College and Engineering Physics Velocity and Speed 3 TOC 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. The velocity of the airplanes has the same magnitude, but a different direction. Velocity

College and Engineering Physics Velocity and Speed 4 TOC The x-component of most vectors (though not all) will be the component which is horizontal (lies along the plane of the earth). Horizontal Motion Position Determines a particle’s location Velocity Determines the direction of the particle’s motion Acceleration Determines the direction of the change in a particle’s motion VariableSymbolNegativePositive Meaning of the Sign y x y x

College and Engineering Physics Velocity and Speed 5 TOC The y-component of most vectors (though not all) will be the component which is vertical (points perpendicular to the plane of the earth). Vertical Motion Position Determines a particle’s location Velocity Determine the direction of the particle’s motion Acceleration Determines the direction of the change in a particle’s motion VariableSymbolNegativePositive Meaning of the Sign y x y x

College and Engineering Physics Velocity and Speed 6 TOC The direction and quantity of “motion” of a particle is given by its velocity. The average velocity of a particle (whether or not the motion is uniform) is given be a simple equation … 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”. The slope of this line is the x-component of the average velocity. Average Velocity x t

College and Engineering Physics Velocity and Speed 7 TOC Velocity is constant if it does not change. This means that the quantity (known as the magnitude) and the direction stay the same. 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. Motion with Constant Velocity (Uniform Motion) x t

College and Engineering Physics Velocity and Speed 8 TOC To model the way a particle moves, we can use a graph of position vs. time. Position vs. Time Graph x t y t y x

College and Engineering Physics Velocity and Speed 9 TOC 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. Velocity vs. Time Graph x t vxvx t 0s5s8s4s7s2s3s6s1s 0s5s8s4s7s2s3s6s1s

College and Engineering Physics Velocity and Speed 10 TOC To determine where an object will be at a later time, we can use velocity vs. time curve. Velocity vs. Time V x (m/s) t (s) TimeVelocityPosition 0 s3 m/s2 m 1s3 m/s5 m 2 s3 m/s8 m 3 s-3 m/s5 m 4 s-3 m/s2 m 5 s-3 m/s-1 m 6 s0 m/s-1 m 7 s0 m/s-1 m 8 s2 m/s1 m

College and Engineering Physics Velocity and Speed 11 TOC To determine where an object will be at a later time, we can use velocity vs. time curve. Position vs. Time x (m) t (s) TimeVelocityPosition 0 s3 m/s2 m 1s3 m/s5 m 2 s3 m/s8 m 3 s-3 m/s5 m 4 s-3 m/s2 m 5 s-3 m/s-1 m 6 s0 m/s-1 m 7 s0 m/s-1 m 8 s2 m/s1 m

College and Engineering Physics Velocity and Speed 12 TOC To determine where an object will be at a later time, we can use velocity vs. time curve. Comparison x (m) t (s) V x (m/s)

College and Engineering Physics Velocity and Speed 13 TOC This is the last slide. Click the back button on your browser to return to the Ebook.