Answer to Question #334098 in Calculus for Kirby

Question #334098

Suppose that a particle moves along a line with position function s(t) =2t^2 +3t+1 where s is in meters and t is in seconds.


a. What is its initial position?

b. Where is it located after t = 2 seconds?

c. At what time is the particle at position s = 6?




1
Expert's answer
2022-04-27T16:33:18-0400

a.


s(0)=s0=2(0)2+3(0)+1=1(m)s(0)=s_0=2(0)^2 +3(0)+1=1(m)

b.


s(2)=2(2)2+3(2)+1=15(m)s(2)=2(2)^2 +3(2)+1=15(m)

15 meters from its initial position.


c.


s(t)=6m,t0s(t)=6 m, t\ge0

2t2+3t+1=62t^2 +3t+1=6

2t2+3t5=02t^2 +3t-5=0

(t1)(2t+5)=0(t-1)(2t+5)=0

t=1 or t=2.5t=1\ or\ t=-2.5

Since t0,t\ge 0, we take t=1s.t=1 s.

The particle will be at position s = 6 after 1 second.


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