# Integration by Parts and Motion in a Particle

A particle is set in motion at time t=0 and moves to the right along the x-axis. (a) Suppose that its acceleration at time t is a=100e^(-1). Show that the particle moves infinitely far to the right along the x-axis. (b) Suppose that its acceleration at time t is a=100(1-t)e^(-1). Show that the particle never moves beyond a certain point to the right of its initial position and find that point. Explain why the particle "effectively" comes to a stop at that point.

Â© BrainMass Inc. brainmass.com March 4, 2021, 8:55 pm ad1c9bdddfhttps://brainmass.com/math/integrals/integration-parts-motion-particle-203863

#### Solution Preview

A particle is set in motion at time t=0 and moves to the right along the x-axis. (a) Suppose that its acceleration at time t is a=100e^(-1). Show that the particle moves infinitely far to the right along the x-axis. (b) Suppose that its acceleration at time t is ...

#### Solution Summary

This provides an example of working with integration by parts and a particle in motion in clearly calculated steps in an attachment.