Final answer:
To find the acceleration when the velocity is zero for the particle with motion described by the function s(t) = t³ - 3t, differentiate the displacement to get the velocity, set it to zero to find the time, and differentiate the velocity to find the acceleration at that time.
Step-by-step explanation:
The equation of motion for a particle is given by s(t) = t³ - 3t, where s is the displacement in meters and t is the time in seconds. To find the acceleration when velocity is zero, we need to first find the velocity function by differentiating the displacement function with respect to time, v(t) = ds/dt = 3t² - 3. Setting the velocity function to zero gives us the time when the velocity is zero. Then we differentiate the velocity function to obtain the acceleration function, a(t) = dv/dt = 6t. Plugging in the time when velocity is zero into the acceleration function gives us the acceleration at that instant.
For example, if the velocity is zero at t = 1 s, then the acceleration is a(1 s) = 6 * 1 s = 6 m/s². However, without knowing the specific time at which the velocity is zero, we cannot give a numerical value for the acceleration.