Science:Math Exam Resources/Courses/MATH100/December 2014/Question 07 (b)
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Question 07 (b) 

Particle moves on the axis starting at the point and travels towards the origin with constant speed of units per second. Particle moves on the axis starting at the origin and travels in a positive direction with constant speed of unit per second.what moment in the first seconds is the distance minimised? 
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 

What possible values of could give the minimum distance? Check these. 
Hint 2 

It may be easier to minimise the distance squared, which is equivalent to minimising the distance. 
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 1 

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Please rate my easiness! It's quick and helps everyone guide their studies. So we need to minimise the distance for . We instead minimise , which is equivalent, using the closed interval method:
The critical numbers are then given by So the only critical number is , for which holds that . Then
By the closed interval method, the minimum distance is reached when seconds. 
Solution 2 

Found a typo? Is this solution unclear? Let us know here.
Please rate my easiness! It's quick and helps everyone guide their studies. So we need to minimise the distance for . We do this using the closed interval method:
The critical numbers are then given by So the only critical number is when . This is at . Then
By the closed interval method the minimum distance is reached when seconds. 