Physics 203 Movie Motion Homework
2-1) Describing velocity changes: In each of the following situations you will be asked to refer to the mathematical definitions and the concepts associated with the number line. Note that being more positive is the same as being less negative and so on.
a) Suppose an object undergoes a change in velocity from -4 m/s to -1 m/s. Is its velocity becoming more positive or less positive? What is meant by more positive? less positive? Is the acceleration positive or negative?
A physical value is said to become more positive if its value is increasing over time. An equivalent definition is that a value becomes more positive if the difference between its final value and its initial value is positive. A geometric representation on the number line (taking the number line direction from left to right) is that the physical value is becoming more positive if its initial value stands to the left of its final value on this line.
For the data in the text since the final value of the speed (-1 m/s) is greater than the initial value (-4 m/s) therefore it is increasing over time, hence is becoming more positive.
Now, by definition the acceleration an object is equal to the change of the value of the speed (between the final and initial states) over the time taken by this change. Since the change in speed is
`Delta(V) = V_f -V_i = -1-(-4) =+3 m/s`
and the time `Delta(t)` taken by the speed change is always positive, then the the acceleration is positive.
`a = (Delta(V))/(Delta(t)) > 0`