(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

A particle has a linearly varying rectilinear acceleration of a=x''i=(12t)i m/s^2. Two observations of the particle's motion are made: Its velocity at t = 1s is x'i=2i m/s, and its position at t= 2s is given bt xi=3i m.

(a) Find the displacement of the particle at t=5s relative to where it was at t = 0s.

(b) Determine the distance traveled by the particle over the same time interval.

2. Relevant equations

3. The attempt at a solution

Given:

x''=12t

x'(1)=2

x(2)=3

Integrate x''=12t and apply initial conditions and get the equations of motion:

x''=12t

x'=6t^2-4

x=2t^3-4t-5

(a) plug in: x(5)-x(0) and get 230m. Correct answer

(b) Isn't it the same thing? x(5)-x(0)? But the book says its 234 m. No idea how this came about.

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# Rectilinear motion (displacement, position) calculus

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