SAT Physics Kinematics in One Dimension - Kinematic Equations

SAT Physics Kinematics in One Dimension - Kinematic Equations

The kinematic equations relate the kinematic variables in a manner that solves for a variety of situations.
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The SAT Subject Test in Physics will not provide you with a list of equations. However, equations are essential when solving numerical problems. They also assist you in analyzing conceptual problems. Therefore, it is in your best interest to memorize the equations used throughout this book. Different resources vary, and you may be familiar with different versions of the equations presented in this text. To simplify the memorization process and to review information specific to the Subject Test in Physics, the most streamlined versions of all equations have been used in this book.

Choosing the Correct Equation
Choosing the correct equation depends on the variables mentioned in each problem. In addition, when an object is initially at rest (vi = 0), the equations simplify into frequently tested, easier versions of the kinematic equations. Table 3.5 will help you identify which equation you should use based on what is given and what is requested in a particular question. It will also help you identify shortened variations of those equations for objects that are initially at rest.
Table 3.5 Choosing Which Kinematic Equation to Use
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Problem Never Mentions Time
Determine the maximum height reached by a ball thrown upward at 20 meters per second.
 
WHAT'S THE TRICK?

Complete a variable list, including known constants and hidden values. In vertical motion problems, y and h are often used in place of displacement, x. In addition, the acceleration of gravity, g, replaces the general acceleration, a. When objects reach “maximum height,” they come to an instantaneous stop (vf = 0 m/s).
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Problem Involves Time and Velocity
A car traveling at 30 meters per second undergoes an acceleration of 5.0 meters per second squared for 3.0 seconds. Determine the final velocity of the car.
 
WHAT'S THE TRICK?

Complete a variable list. If variables seem to be missing, read the problem again and look for key phrases signaling hidden variables. The problem did not state how the acceleration was affecting the car, so you must assume the simplest scenario. Unless the problem specifies a decrease in speed, assume acceleration is positive and that it acts to increase speed.
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Problem Involves Time and Displacement
A ball is dropped from a 45-meter-tall structure. Determine the time the ball takes to hit the ground.
 
WHAT'S THE  TRICK?

Complete a variable list, including known constants and hidden values.
A “dropped” object has an initial velocity of zero (v, = 0 m/s). The structure is 45 m tall, and the ball is moving downward toward the ground (y = -45 m). The acceleration is due to gravity, which also acts downward (g = -10 m/s2).
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KINEMATIC GRAPHS
Interpreting graphs and determining their significance is discussed at length in Chapter 1, “Conventions and Graphing.” The key values to assess are slope, area, and intercepts. To determine if slope or area is important, remember to include units in your calculations. In addition, it may also be important to determine if values are constant or changing. Table 3.6 describes frequently used graphs involving the kinematic formulas and variables.
Table 3.6 Graphs and Kinematics
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The velocity versus time graph described in Table 3.6 contains the most information, making it the most valuable and most frequently tested kinematic graph.
Analyzing Velocity versus Time Graphs
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The motion of an object is shown in the velocity versus time graph above.
(A) Determine the initial velocity of the object.
 
WHAT'S THE TRICK?

Initial conditions occur at zero time. In graphs with time along the x-axis, initial values are the y-intercept. The initial velocity is 20 m/s.
(B) Describe the motion during the first second.
 
WHAT'S THE  TRICK?

The horizontal line indicates that the independent variable, velocity, remains
constant. The motion during the first second is constant velocity.
(C) Determine the displacement during the first second.
 
WHAT'S THE TRICK?

Displacement is the area under the velocity versus time graph.
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(D) Determine the acceleration in the time interval between 1 and 4 seconds.
 
WHAT'S THE TRICK?

Acceleration is the slope of the velocity versus time graph.
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(E) Determine the final speed of the object.
 
WHAT'S THE TRICK?

Simply read the graph. At the end of 5 seconds, the object has a velocity of -10 m/s. However, the question asks for speed. Speed is a scalar representing the magnitude of velocity. Speed is the absolute value of the velocity, 10 m/s.
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