2. Motion in two dimensions, including projectile motion a) Students should be able to add, subtract and resolve displacement and velocity vectors, so they can: 1) Determine components of a vector along two specified, mutually perpendicular axes . 2) Determine the net displacement of a particle or the location of a particle relative to another . 3) Determine the change in velocity of a particle or the velocity of one particle relative to another . b) Students should understand the general motion of a particle in two dimensions so that, given functions x ( t ) and y ( t ) which describe this motion, they can determine the components, magnitude and direction of the particle’s velocity and acceleration as functions of time . c) Students should understand the motion of projectiles in a uniform gravitational field, so they can: 1) Write down expressions for the horizontal and vertical components of velocity and position as functions of time, and sketch or identify graphs of these components . 2) Use these expressions in analyzing the motion of a projectile that is projected with an arbitrary initial velocity . B. Newton’s laws of motion 1. Static equilibrium (first law) Students should be able to analyze situations in which a particle remains at rest, or moves with constant velocity, under the influence of several forces . 2. Dynamics of a single particle (second law) a) Students should understand the relation between the force that acts on an object and the resulting change in the object’s velocity, so they can: 1) Calculate, for an object moving in one dimension, the velocity change that results when a constant force arrowrightnosp F acts over a specified time interval . 2) Calculate, for an object moving in one dimension, the velocity change that results when a force arrowrightnosp F t ( ) acts over a specified time interval . 3) Determine, for an object moving in a plane whose velocity vector undergoes a specified change over a specified time interval, the average force that acted on the object . b) Students should understand how Newton’s second law, arrowrightnosp arrowrightnosp arrowrightnosp F F ma net Â = = , applies to an object subject to forces such as gravity, the pull of strings, or contact forces, so they can: 1) Draw a well-labeled, free-body diagram showing all real forces that act on the object . 2) Write down the vector equation that results from applying Newton’s second law to the object, and take components of this equation along appropriate axes .
18 © 2014 The College Board. Visit the College Board on the Web: . c) Students should be able to analyze situations in which an object moves with specified acceleration under the influence of one or more forces so they can determine the magnitude and direction of the net force, or of one of the forces that makes up the net force, such as motion up or down with constant acceleration .
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