Posted by **Yoona** on Sunday, November 20, 2011 at 2:37pm.

A particle moves along the c-axis so that at time t its position is given by x(t)=t^2-6^t+9t+11

a)What is the velocity of the particle at t=0

b)During what time intervals is the particle moving to the left?

c)What is the total distance traveled by the particle t=0 to t=2

- Calculus - Correction? -
**Steve**, Sunday, November 20, 2011 at 2:53pm
I can't believe that is the correct equation of motion. 6^t will grow negative quite quickly. Since there's a typo in c-axis, I suspect there's another in the equation.

- Calculous -
**Yoona**, Sunday, November 20, 2011 at 2:55pm
opps it is x(t)=t^3-6t^2+9t+11

Sorry!!

- Calculus -
**Steve**, Sunday, November 20, 2011 at 4:09pm
That's better!

x(t) is the position

x'(t) is the velocity

x'(t) = 3t^2 - 12t + 9

x'(0) = 9

particle moving to the left means velocity is negative.

3(t^2 - 4t + 3) = 3(t-1)(t-3) < 0

when 1 < t < 3

distance traveled is x(2) - x(0)

- Calculous -
**Yoona**, Sunday, November 20, 2011 at 4:55pm
thanks!!! that was VERY helpful!!

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