Problem 12-10: Engineering Mechanics- Dynamics (Hibbeler 14th Edition)

Finding Particle Velocity by Numerical Integration of a Position-Dependent Acceleration

This lesson demonstrates how to find a particle's velocity at a given position when acceleration is a nonlinear function of position. The kinematic relation v dv = a ds is used to set up a definite integral, which is then evaluated numerically using Simpson's 1/3 Rule with four subintervals.

Question:
A particle moves along a straight line with an acceleration of a equals 5 divided by the quantity 3 times s to the one-third power plus s to the five-halves power, in meters per second squared, where s is in meters. Determine the particle's velocity when s equals 2 meters, given that it starts from rest when s equals 1 meter. Use a numerical method to evaluate the integral.

In this lesson, you will learn to:
• Apply the kinematic relationship a = v dv/ds to separate variables and set up a definite int