Science:Math Exam Resources/Courses/MATH110/April 2019/Question 01 (b)

MATH110 April 2019

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Question 01 (b)

Suppose the position (in metres) of an object moving in a straight line at time $t$ (in seconds) is given by a function $f(t)$ such that $f'(1)=2$ and $f''(1)=-1$ , then (a) the object’s velocity at $t=1$ is 2 m/s and the object is speeding up. (b) the object’s velocity at $t=1$ is 2 m/s and the object is slowing down. (c) the object’s velocity at $t=1$ is −1 m/s and the object is speeding up. (d) the object’s velocity at $t=1$ is −1 m/s and the object is slowing down.

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
Recall the physical interpretation of derivative and second derivative.

Hint 2
The first derivative represents velocity. The second represents 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. The first derivative is 2, so the object's velocity is 2 m/s. The second derivative is negative, so acceleration is negative, and the object is slowing down. The answer is (b).

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