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January 30, 2015

January 30, 2015

Posted by **Matt** on Monday, February 7, 2011 at 6:28pm.

a.) Where is the particle when it is at rest?

b.) During what time interval is the particle moving to the LEFT?

c.) When is the acceleration lest?

d.) What is the TOTAL distance traveled by the particle from t=0 to t=3 ?

- Calculus-particle motion -
**Damon**, Monday, February 7, 2011 at 8:53pma) at rest means dx/dt = 0

12 t^2 -32 t + 15 = 0

t = 2.05 or .607

find x for those two values of t

b) where is dx/dt negative

do a sketch of dx(t)/dt =12t^2-32t+15

you know it is a parabola facing up (holds water) because of the positive coef of x^2

You know it is 0 at t = 2.05 and .607

so it is negative between those two times.

c) a = d^2x/dt^2 = 24 t -32

that seems to be least for t = 0 unless it means |a| which is 0 at t = 32/24

d) integral from 0 to 3 of original function is

value of t^4 - (16/3)t^3 +(15/2)t^2

when t = 3

(since it is 0 at t = 0)

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