Question

Rectilinear Motion:
*Need help with these three!*

Directions: The position function of a particle moving on a coordinate line is given by the following eq'ns, where s is in feet and t is in sec. Describe the motion of the particle for any time. Make a DIAGRAM of the motion with respect to its position at time t.

1.) s(t) =t^3 -6t^2

3.) s(t) = 1+6t -t^2

5.) s(t)=t^3 -9t^2 +24t

Answer 1

#1 is t^2(t-6)
ds/dt = 3t^2-12t = 3t(t-4)
Since s(t) it has a double root at t=0, it starts by moving down, then up again at t=4.

#2 is just a parabola, with s(0) = 1
since ds/dt > 0 at t=0, s increases until t=3, then decreases from there

#3 ds/dt = 3t^2-18t+24 = 3(t-2)(t-4)
so, s(0) = 0, and s increases while 0<t<2, decreases where 2<t<4, then increases again from there.

Go to any good online graphing site and you can see the graphs.