# particle velocity

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.

https://brainmass.com/math/calculus-and-analysis/particle-velocity-harmonic-motion-443486

#### Solution Summary

This solution assesses particle velocity. Particle velocity and harmonic motion is examined for particles.