Final answer:
The acceleration of the particle when t=3 s is calculated by differentiating the velocity function and substituting t=3 s into the resulting acceleration function, yielding an acceleration of 5.5 m/s².
Step-by-step explanation:
The acceleration of a particle is found by differentiating its velocity function with respect to time. Given the velocity function v = (0.5t³ − 8t) m/s, the acceleration a(t) is the derivative dv/dt. Thus, the steps to calculate the acceleration at t=3 s are as follows:
Take the derivative of v with respect to t to get a(t):
a(t) = d(0.5t³ − 8t)/dt = 1.5t² − 8.
Substitute t = 3 s into the acceleration function a(t):
a(3 s) = 1.5(3)² − 8 = 1.5(9) − 8 = 13.5 − 8 = 5.5 m/s².
Therefore, the acceleration of the particle when t=3 s is 5.5 m/s².