Final answer:
The acceleration of the particle at t = 2 seconds, given the velocity function v = 2t³ - 4t m/s, is 20 m/s².
Step-by-step explanation:
The acceleration of a particle moving along the x-axis is determined by the rate of change of its velocity function. Given the velocity function v = 2t³ - 4t m/s, we can find the acceleration by taking the first derivative of the velocity with respect to time t.
The derivative of 2t³ with respect to t is 6t², and the derivative of -4t is -4.
Therefore, the acceleration function a(t) is given by a(t) = 6t² - 4. Substituting t = 2 s into this function gives us a(2s) = 6(2)² - 4, which simplifies to a(2s) = 6(4) - 4 = 24 - 4 = 20 m/s². Thus, the acceleration of the particle at t = 2 seconds is 20 m/s².