Final Answer:
The position of the particle at time t is given by the equation s(t) = 2t² - 5t + 3.
Step-by-step explanation:
The given position function is s(t) = 2t² - 5t + 3. This is a quadratic function representing the position of the particle as a function of time. The variable t represents time, and s(t) represents the position of the particle at time t.
In the equation, the coefficient of t² is 2, indicating that the particle's motion is influenced by a quadratic term. The coefficient of the linear term (-5t) represents the velocity of the particle, and the constant term (3) is the initial position of the particle at time t = 0.
To find the time at which the particle is at a certain position, one can set s(t) equal to that position and solve for t. For example, if asked when the particle is at position 10, you would set 2t² - 5t + 3 equal to 10 and solve for t.
In summary, the position function s(t) = 2t² - 5t + 3 provides a mathematical expression for the particle's position at any given time t. This quadratic equation allows for the analysis of the particle's motion, including determining its position at specific points in time.
Complete Question:
How does the position function, s(t) = 2t² - 5t + 3, enable the analysis of the particle's motion, and what steps would you take to find the time at which the particle is at a certain position, such as when it is at position 10?