1.3 Representing Motion

Describe the position, velocity, and acceleration of an object using representations of that object’s motion.

• Motion can be represented by motion diagrams, figures, graphs, equations, and narrative descriptions.
• For constant acceleration, three kinematic equations can be used to describe instantaneous linear motion in one dimension: vvxx=+ 0 atx vv2 xx=+ 2 0 2axx () −x 0 1xx =+00 vtxx +at 2 2 Note: The equations above are written to indicate motion in the x-direction, but these equations can be used in any single dimension as appropriate.
• Near the surface of Earth, the vertical acceleration caused by the force of gravity is downward, constant, and has a measured value approximately equal to
• Graphs of position, velocity, and acceleration as functions of time can be used to find the relationships between those quantities. TOPIC 1.3 Representing Motion
  • i. An object’s instantaneous velocity is the rate of change of the object’s position, which is equal to the slope of a line tangent to a point on a graph of the object’s position as a function of time. Relevant equation: dxvx = dt
  • ii. An object’s instantaneous acceleration is the rate of change of the object’s velocity, which is equal to the slope of a line tangent to a point on a graph of the object’s velocity as a function of time. Relevant equation: dva x x = dt
  • iii. The displacement of an object during a time interval is equal to the area under the curve of a graph of the object’s velocity as a function of time (i.e., the area bounded by the function and the horizontal axis for the appropriate interval). Relevant equation: 1
  • iv. The change in velocity of an object during a time interval is equal to the area under the curve of a graph of the acceleration of the object as a function of time. Relevant equation: BOUNDARY STATEMENT AP Physics C: Mechanics and AP Physics C: Electricity and Magnetism expects that for all situations in which a numerical quantity is required for g, the value g 10 m/ s2 will be used. However, students will not be penalized for correctly using the more precise commonly accepted values of g= 9.81 m/ s2 or g= 9. 8m /s2.