Science:Math Exam Resources/Courses/MATH100/December 2013/Question 03 (b)
• Q1 (a) • Q1 (b) • Q1 (c) • Q1 (d) • Q2 (a) • Q2 (b) • Q2 (c) • Q3 (a) • Q3 (b) • Q3 (c) • Q4 (a) • Q4 (b) • Q4 (c) • Q5 • Q6 • Q7 • Q8 (a) • Q8 (b) • Q8 (c) • Q8 (d) • Q9 • Q10 (a) • Q10 (b) • Q11 •
Question 03 (b) 

ShortAnswer Question. Simplify your answer as much as possible and show your work. Let be the position function of a particle that is moving in a straight line, where t is measured in seconds and s in metres. When is the particle moving in the negative direction? 
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 hints below. Read the first one and consider it for a while. Does it give you a new idea on how to approach the problem? If so, try it! If after a while you are still stuck, go for the next hint. 
Hint 1 

When the particle is moving in the negative direction (backwards), what function of time is negative? (It is not position!) 
Hint 2 

What is the definition of the velocity function? How does it relate to the position function? 
Checking a solution serves two purposes: helping you if, after having used all the hints, you still are stuck on the problem; or if you have solved the problem and would like to check your work.

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. When the particle is moving in the negative direction, its velocity is negative. Therefore we must look for the for which :
Plugging in values tells us that on the interval , where is in seconds as stated above. 