Given the following position function:
(position is in ft , time is in sec)

Find the velocity at

Round your answer to the nearest thousandth

Ask by Daniels Vaughn. in the United States

Jan 24,2025

Question

Given the following position function:
(position is in ft , time is in sec)

Find the velocity at

Round your answer to the nearest thousandth

Ask by Daniels Vaughn. in the United States

Jan 24,2025

UpStudy AI · Accepted Answer

To find the velocity at $$ t = 0.5 $$ seconds, we need to find the derivative of the position function $$ s(t) = \tan(t^2) $$ with respect to time $$ t $$.

The derivative of $$ \tan(t^2) $$ with respect to $$ t $$ is given by:
$$ \frac{d}{dt} \tan(t^2) = \frac{2t}{\cos^2(t^2)} $$

Now, we can substitute $$ t = 0.5 $$ into the derivative to find the velocity at that time:
$$ v(0.5) = \frac{2(0.5)}{\cos^2((0.5)^2)} $$

Let's calculate the velocity at $$ t = 0.5 $$ seconds.
Simplify the expression by following steps:
- step0: Solution:
  $$\frac{2\times 0.5}{cos^{2}\times 0.5^{2}}$$
- step1: Multiply by $$a^{-n}:$$
  $$\frac{2\times 0.5\times 0.5^{-2}}{cos^{2}}$$
- step2: Multiply:
  $$\frac{4}{cos^{2}}$$
The velocity at $$ t = 0.5 $$ seconds is approximately $$ 1.065199 $$ ft/sec.

Rounding this to the nearest thousandth, the velocity at $$ t = 0.5 $$ seconds is approximately $$ 1.065 $$ ft/sec.
The velocity at $$ t = 0.5 $$ seconds is approximately $$ 1.065 $$ ft/sec.

Given the following position function:
(position is in ft , time is in sec)

Find the velocity at

Round your answer to the nearest thousandth

Upstudy AI Solution

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Solution

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Given the following position function: (position is in ft , time is in sec) Find the velocity at Round your answer to the nearest thousandth

Upstudy AI Solution

Answer

Solution

Beyond the Answer

Related Questions

Latest Calculus Questions

Given the following position function:
(position is in ft , time is in sec)

Find the velocity at

Round your answer to the nearest thousandth