https://file.aiquickdraw.com/mathbot/file/17265397191859hj73x97.jpg

We are asked to find the instantaneous velocity of the particle after 2 seconds, given that the derivative of the position function \( s(t) \), which is the velocity function \( s'(t) \), is:

\[
s'(t) = 2t^2 - 4t + 3
\]

To find the instantaneous velocity at \( t = 2 \), we need to substitute \( t = 2 \) into \( s'(t) \).

\[
s'(2) = 2(2)^2 - 4(2) + 3
\]
\[
s'(2) = 2(4) - 8 + 3
\]
\[
s'(2) = 8 - 8 + 3
\]
\[
s'(2) = 3
\]

Thus, the instantaneous velocity at \( t = 2 \) seconds is \( 3 \). The correct answer is **3**.

Do you want any further details or have questions?

Here are 5 related questions:
1. What is the general meaning of instantaneous velocity?
2. How do you interpret the position function in terms of particle motion?
3. What would happen if we needed to find the velocity at \( t = 0 \)?
4. How do we find the acceleration from the velocity function?
5. What if the position function \( s(t) \) was given directly—how would you find velocity?

**Tip:** The instantaneous velocity is always the derivative of the position function at a specific time.

Suppose a particle moves along the x-axis and that its position after t seconds is given by the function s(t). Suppose further that the derivative of s(t) is given by s'(t) = 2t^2 - 4t + 3. What is the instantaneous velocity of the particle after 2 seconds?

Learn how to calculate the instantaneous velocity of a particle at a specific time, given the derivative of its position function s(t). The problem involves understanding key calculus concepts like derivatives and instantaneous velocity, suitable for Grades 11-12 or introductory college calculus.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation