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APA
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Mathematics & Economics
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English (U.S.)
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Topic:

Finding Derivatives, Distance, and Instantaneous Velocity

Coursework Instructions:

The distance s (in ) above the ground for a projectile fired vertically upward with a velocity of 4 as a function of time t (in ) is given by. s=4[a]t-4.9t^2
my instructor has provided you with a which is 3. Simply replace the letter with the corresponding digit. Do not multiply. For example, if [a]=3, then 4[a] is 43.
Find the answers to these questions.
find t for v=0
find v for t =4
find v for t =5
What conclusions can you draw?
State the value you are using for a before you show the work to answer these four questions. Remember to use the Canvas Equation Editor. Refer to the Tools for Mathematics page in the Course Specific Information module for technical guidance. Post your answers in the discussion area by the end of the fourth day of the module week.
Review & Discuss
Compare and contrast your work to that of your classmates. Engage in a dialogue, addressing one or more of the following areas:
Do you agree with the work and explanations?
Where are the errors in the proposed solutions (mine or classmates')?
Which solution is correct? Why? Is there more than one way to get to the correct solution?
Are some of the explanations clearer than others? What makes them easier to understand?
Do you have suggestions for improvement?
Have we each given thorough explanations for our work?
Which way is easier?

Coursework Sample Content Preview:
Math 112 Discussion:
The value for a is 3. Hence the equation is s=43t-4.9t2.
1 Find t for v=0.
Solution: Since s represents the displacement, and t represents the time for objects moving with rectilinear motion, the derivative of s with respect to t will give a function for the instanteneus velocity.
Also, we know that dsdt=0.
Step 1. Find the derivative of the first term.
Therefore, 43t=ddx43t=43ddtt=43
Step 2. Find the derivative of the second term.
Therefore, -4.9t2=ddt-4.9t2=-4.9ddtt2=-4.92t=9.8t
Step 3. Then dsdt=43-9.8t.
Since we know that v=0, and t is unknown, equate the equation to zero.
Therefore, dsdtt=?
To solve for t, 43-9.8t=0
9.8t=43
t=4.39s
Answer: when v=0, t=4.39s
(Distance in m) s=43t-4.9t2
Therefore, (Distance in m) s=434.39-4.9(4.39)2
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