document.write( "Question 1175915: The position of a particle is given as s(t) = 2/5t^5 −2t^4 + 2t^3 where t is in hours and s(t) is in miles.\r
\n" ); document.write( "\n" ); document.write( "Find the velocity of the particle.
\n" ); document.write( "Find the acceleration of the particle
\n" ); document.write( "When is the particle at rest?
\n" ); document.write( "When is the particle moving forward?
\n" ); document.write( "When is the particle moving backward? \n" ); document.write( "
Algebra.Com's Answer #801732 by Boreal(15235)\"\" \"About 
You can put this solution on YOUR website!
velocity is ds/dt=2t^4-8t^3+6t^2
\n" ); document.write( "acceleration is d^2s/dt^2=8t^3-24t^2+12t
\n" ); document.write( "at rest when the velocity is 0
\n" ); document.write( "moving forward with v>0
\n" ); document.write( "backward with v<0.
\n" ); document.write( "0=2t^2(t^2-4t+3)=2t^2((t-1)(t-3))
\n" ); document.write( "so at t=1 sec and t=3 sec it is at rest.
\n" ); document.write( "when t is 2 seconds, the function ds/dt is negative, so it is moving backward. After 3 seconds, it is moving forward, and before 1 second it is moving forward.\r
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