A particle moves according to a law of motion s = f(t), 0 < and = t< and = 6, wh

Question

A particle moves according to a law of motion s = f(t), 0 < and = t< and = 6, where t is measured in seconds and s in feet. f(t) = cos(pi*t/3)

(a) Find the velocity at time t (in ft/s).
v(t) =  

(b) What is the velocity after 1 s? (Round your answer to two decimal places.)
v(1) =  ft/s

(c) When is the particle at rest?

(d) When is the particle moving in the positive direction? (Enter your answer using interval notation.)


(e) Find the total distance traveled during the first 6 s.
ft

(f) Find the acceleration at time t (in ft/s2).

a(t) =

Find the acceleration after 1 s. (Round your answer to two decimal places.)

a(1) =  ft/s2

(g) Graph the position, velocity, and acceleration functions for 0 ? t ? 6.

(h) When is the particle speeding up? (Enter your answer using interval notation.)


When is it slowing down? (Enter your answer using interval notation.)

Explanation / Answer

a)velocity:-pi/3*sin(pi*t/3)

b)after 1 sec velocity :-(pi/3)*(sqrt(3)/2)

c)t=small value,at t=0 velocity is zero

d)after 3 secs

e)3/pi*4

f)accelration=-pi2/9*cos(pi*t/3)

g)to the right top graph

h)1.5 to 3(going up)

3 to 4.5 (slowing down)

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