# Calculous

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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? -

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 -

opps it is x(t)=t^3-6t^2+9t+11
Sorry!!

• Calculus -

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 -

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