Science:Math Exam Resources/Courses/MATH110/December 2016/Question 06 (c)

MATH110 December 2016

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Question 06 (c)

Explorers on a small airless planet used a spring gun to launch a small ball vertically upward from the ground at a launch velocity of $15{\text{m}}/{\text{s}}$. The explorers expected the ball to reach a height of $$s(t)=15t-(1/2)gt^{2}$$ metres at $t$ seconds after being launched, where $g$ is a constant. (c) Sketch the graph of the ball’s acceleration $a(t)$ for $0\leq t\leq 40$. Make sure you indicate the values of any intercepts, if they exist.

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

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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. By Hint, the acceleration is a derivative of the velocity; $$a(t)=v'(t)=\left(15-{\frac {3}{4}}t\right)'=-{\frac {3}{4}}$$ . Plugging $t=0$, we get a $y$-intercept $y=-{\frac {3}{4}}$. On the other hand, since $a(t)$ only has its function value $-{\frac {3}{4}}$, there's no points whose function value is $0$. In other words, there's no $x$-intercepts. Since it is a constant function, we can easily draw its graph as follows.