# instantenous motion

• Mar 14th 2007, 01:54 PM
qbkr21
instantenous motion
Guys as always I appreciate you help. I think this is one of the best sites on the internet. I do however have a question:

A particle moves along a straight line and its position at time t s given by s(t)= 2t^3 - 15 t^2 + 24 t where s is measured in feet and t in seconds. Find the velocity (in ft/sec) of the particle at time t=0___?___. The particle stops moving twice, once when t=A and again when t=B where A<B. A is ___?____
& B is ___?___. What is the position of the particle at time 10 ___?____.

Thanks Again!
• Mar 14th 2007, 02:16 PM
CaptainBlack
Quote:

Originally Posted by qbkr21
Guys as always I appreciate you help. I think this is one of the best sites on the internet. I do however have a question:

A particle moves along a straight line and its position at time t s given by s(t)= 2t^3 - 15 t^2 + 24 t where s is measured in feet and t in seconds. Find the velocity (in ft/sec) of the particle at time t=0___?___. The particle stops moving twice, once when t=A and again when t=B where A<B. A is ___?____
& B is ___?___. What is the position of the particle at time 10 ___?____.

Thanks Again!

It's velocity is ds/dt = 6 t^2 -30 t +24, so at t=0 ds/dt=24 ft/s.

The particle stops moving when ds/dt=0, but:

ds/dt = 6 t^2 -30 t +24 = (t-1)(6t-24)

so ds/dt = 0, when t=1 s, and again when t=4 s, so A=1, and B=4.

Now s(t)= 2t^3 - 15 t^2 + 24 t, so at t=10:

s(10) = 2*1000 - 15*100 + 24*10 = 740 ft.

RonL