Science:Math Exam Resources/Courses/MATH110/April 2017/Question 01 (c)

MATH110 April 2017

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Question 01 (c)
If the acceleration of an object is negative (and the object is not momentarily stopped), at that particular instant the object can be (A) slowing down. (B) speeding up. (C) either slowing down or speeding up–not enough information to determine.

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
If the position of an object is given by $f(t)$ after $t$ units of time, what is the velocity of the object? what is the acceleration?

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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. If $f(t)$ represents the position of an object at time $t$, then the first derivative of $f(t)$ is the velocity of the object. The second derivative of $f(t)$ is the derivative of $f'(t)$, the velocity, and by definition this is the object's acceleration. Now he acceleration of an object is negative, which is saying $f''(t)<0$, thus $f'(t)$ is decreasing, velocity is decreasing. The information in this problem is enough to determine it is speeding down, exclude c answer: $\color {blue}(A)$