Science:Math Exam Resources/Courses/MATH103/April 2014/Question 01 (c) iii

MATH103 April 2014

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Question 01 (c) iii
The graph below depicts the velocity of a car traveling along a straight road as a function of time, $v(t)=\sin(2\pi t)$. Initial time is $t=0$. Graph of 1-c) Determine whether the following statement is True, False, or Indeterminate: The car is moving away from its initial position when $t=5/4$.

Make sure you understand the problem fully: What is the question asking you to do? Are there specific conditions or constraints that you should take note of? How will you know if your answer is correct from your work only? Can you rephrase the question in your own words in a way that makes sense to you?

If you are stuck, check the hint below. Consider it for a while. Does it give you a new idea on how to approach the problem? If so, try it!

Hint
Use the result of part (ii).

Checking a solution serves two purposes: helping you if, after having used the hint, you still are stuck on the problem; or if you have solved the problem and would like to check your work. If you are stuck on a problem: Read the solution slowly and as soon as you feel you could finish the problem on your own, hide it and work on the problem. Come back later to the solution if you are stuck or if you want to check your work. If you want to check your work: Don't only focus on the answer, problems are mostly marked for the work you do, make sure you understand all the steps that were required to complete the problem and see if you made mistakes or forgot some aspects. Your goal is to check that your mental process was correct, not only the result.

Solution

Found a typo? Is this solution unclear? Let us know here. Please rate my easiness! It's quick and helps everyone guide their studies. As seen in the previous part, at time $t=1$, the car is back at its initial position. During the interval $[1,1.5]$, the velocity curve is above the $t$-axis, hence the velocity is positive. Thus, the car is moving away from its initial position during this entire time interval. Since the time $5/4=1.25$ occurs within this interval, the car is moving away from its initial position at that time. The statement is true. Note: A common mistake is interpreting the negative slope of the graph at (1.25,1.5) as the car returning to its original position. Keep in mind, the graph is illustrating the velocity of the car, not its displacement.