ChemPhys 173/273

Unit 6: 1-Dimensional Kinematics

Problem Set C

Overview:

Problem Set C targets your ability to interpret and analyze velocity-time plots representing an object's motion in order to answer questions regarding acceleration, displacement and time.

Velocity-time plots represent variations in an object's velocity over the course of time. As such, the slope of such graphs provides a velocity change-to-time ratio; this ratio represents the acceleration of the object. Many of the questions on this set of problems will test your ability to use the coordinates for two points on a line to determine the slope. The slope is simply the change in the y coordinates divided by the change in the x-coordinate.

Velocity-time plots can also be used to determine the distance traveled by an object and the displacement of an object. The area between a plotted line and the time axis (which could be a positive or a negative value) represents the displacement of the object. The area spoken of here is formed by the plotted line, the time axis and two imaginary vertical lines drawn at two specified points in time. The resulting area could be represented by either a rectangle, a triangle, a trapezoid or a collection of such shapes. The graphic below depicts a variety of resulting shapes and the appropriate formulas for calculating areas from each of them. Note that a complex shape (as shown in the rightmost graph) can be broken into a collection of smaller shapes.

To be successful on this problem set, you will need to be able to:

• calculate slopes of lines from the x-y coordinates of two points.
• calculate the areas between lines and the time axis for various shapes - rectangles, triangles, trapezoids and complex shapes.
• recognize that a negative area (and thus negative displacement) is obtained for a line that extends below the time axis.
• perform some complex algebraic analysis (problems14 and 18).

The following pages from The Physics Classroom tutorial may serve to be useful in assisting you in the understanding of the concepts and mathematics associated with these problems.

Meaning of Shape for a v-t Graph | Meaning of Slope for a v-t Graph | Relating the Shape to the Motion

View Sample Problem Set.

 Problem Description Audio Link 1 A routine slope calculation 2 A routine slope calculation, but often missed due to the common error of taking a y/x ratio (as opposed to delta y/delta x ratio). 3 Performing a routine slope calculation when one of the coordinate values is difficult to read 4 Three routine slope calculations in a single problem; many coordinate values are difficult to read 5 Performing a routine slope calculation when one of the coordinate values is difficult to read 6 A routine area calculation; help file includes a useful animation 7 An area calculation for a complex shape; help file includes a useful animation 8 An area calculation for a complex shape; help file includes a useful animation 9 An area calculation for a complex shape; help file includes a useful animation 10 Carefully interpretting a velocity-time plot in light of one's understanding of direction change 11 An area calculation for a complex shape; help file includes a useful animation. 12 Carefully interpretting a velocity-time plot in light of one's understanding of direction change. 13 Multiple slope calculations for the various phases of a complex motion. 14 Use of area for a motion involving a direction change in order to determine the time of return to an original position. 15 Multiple slope calculations for the various phases of a complex motion. 16 Multiple area calculations for the various phases of a complex motion to determine the overall displacement. 17 Multiple area calculations for the various phases of a complex motion to determine the overall displacement. 18 Complex analysis of two cars moving simulaneously in order to determine the time at which one car is so far ahead of the other. 19 A conceptual question; the database creates a randomly-generated phrase which varies from student to student. 20 A conceptual question; the database creates a randomly-generated phrase which varies from student to student.

Audio Help for Problem: 1 || 2 || 3 || 4 || 5 || 6 || 7 || 8 || 9 || 10 || 11 || 12 || 13 || 14 || 15 || 16 || 17 || 18 || 19 || 20

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