**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).

**Additional Readings/Study
Aids:**

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.

Determining the Slope on a v-t Graph | Determining the Area on a v-t Graph

View Sample Problem Set.

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