Question

What is the position of the moving particle at time t, as described by the position function f(t) = -9t - t^2 - 0.3t^3 + 0.1t^4, when t is greater than or equal to 0?

Answer 1

The position of the particle at any time t can be found by substituting t into the given position function, and displacement is found by subtracting the position at two different times.

Step-by-step explanation:

To find the position of the moving particle at any time t, you simply substitute the time t into the given position function f(t) = -9t - t2 - 0.3t3 + 0.1t4. This polynomial function can be used to determine the position at any given time as long as t ≥ 0. To illustrate how to do this, consider finding the position at t = 5 seconds: we plug in 5 for t in the function, getting f(5) = -9(5) - 52 - 0.3(5)3 + 0.1(5)4, and calculate the result to obtain the particle's position at t = 5 seconds.

Displacement can also be found by subtracting the position function values at different times. For example, for a particle with position given by x(t) = 4 - 2t, the displacement from t = 3 to t = 6 seconds would be x(6) - x(3).