You are in your Physics lab and your professor has an experiment set up to help you learn about harmonic motion. The set up is that you have 112.5/pi^2 (approxmately 11.39 kg) on a frictionless surface that is attached to a spring constant 12.5 N/m. You pull the block to 3/pi meters (approximately .955 meters) such that x(0) = 3/pi and then let go, at which point the block begins to oscillate back and forth.
The velocity of the particle is given by v(t) = sin(pi/3(t)) where t (greater or equal to) 0. Your professor needs you to answer the following questions related to the experiment.
(a) What is the acceleration of the particle at time t = 4? Give an exact answer.
(b) What is the total distance traveled by the particle over the time interval 0 (less than or equal to) t (less than or equal to) 4? Round your answer to three decimal places.
(c) What is the position of the particle at time t = 4? Round your answer to three decimal places.
(d) Below are two statements:
Statement 1: For 3 < t < 4.5, the velocity of the particle is decreasing
Statement 2: For 3 < t < 4.5, the speed of the particle is incresing.
Are either or both of these statements correct? For each, provide a reason why it is correct or not correct.
This solution assesses particle velocity. Particle velocity and harmonic motion is examined for particles.