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The height at time t (in seconds) of a mass, oscillating at the end of a spring, is given by s(t) = 300 + 30sin(t) cm. Find the velocity and acceleration at t = π/3 s.

User Machump
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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.

User Ellotheth
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