Final answer:
To find velocity and acceleration, we take the derivative of the position equation with respect to time. For t = π/3 s, the velocity is 15 cm/s, and the acceleration is -15√3 cm/s² in Simple Harmonic Motion.
Step-by-step explanation:
The question asks to find the velocity and acceleration at a certain point in time for a mass oscillating at the end of a spring, which is an example of Simple Harmonic Motion (SHM). In SHM, the position at any time t can be described by a sine or cosine function. To find the velocity, we differentiate the position equation s(t) = 300 + 30sin(t) cm with respect to time t. The velocity v(t) is hence given by v(t) = 30cos(t). To find the acceleration, we differentiate the velocity equation with respect to time which gives us a(t) = -30sin(t). At t = π/3 s, the velocity v(π/3) is 30cos(π/3)=15 cm/s and the acceleration a(π/3) is -30sin(π/3) = -15√3 cm/s².