Question

A particle is moving along a coordinate axis such that its position is defined as (s(t) = 4t³ - 2t² - 14), where (t ≥ 0). Find the rate at which the particle's position is changing at (t = 3).

a) 96
b) 76
c) 48
d) 30

Answer 1

The rate at which the particle's position is changing at t = 3 is 96.

Step-by-step explanation:

The rate at which the particle's position is changing is given by the derivative of the position function with respect to time. Taking the derivative of the position function s(t) = 4t³ - 2t² - 14 will give us the velocity function v(t).

Then, we can evaluate v(3) to find the rate at which the particle's position is changing at t = 3. Let's calculate it.

Taking the derivative of s(t), we get v(t) = 12t² - 4t. Evaluating v(3), we have v(3) = 12(3)² - 4(3) = 108 - 12 = 96.

Therefore, the rate at which the particle's position is changing at t = 3 is 96.