Question 347251
{{{s(t)=int(v(t),dt)}}}
{{{s(t)=int((-5+30e^(-0.5t)),dt)}}}
{{{s(t)=-5-(30/(1/2))e^(-0.5t)+C}}}
{{{s(t)=-5-60e^(-0.5t)+C}}}
When t=0, s(0)=0.
{{{s(0)=-5-60+C=0}}}
{{{C=65}}}
{{{s(t)=-5-60e^(-0.5t)+65}}}1
{{{highlight(s(t)=60-60e^(-0.5t))}}}
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b)
{{{graph(300,300,-2,12,-10,90,60-60e^(-0.5x),60,30)}}}
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c)I'll leave that part to you.
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d)Oh no. The truck doesn't stop until s=60m (the green line). 
Poor Blinky never had a chance (he was standing at the blue line).
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e)Find {{{t}}} when {{{s(t)=30}}}.
{{{60-60e^(-0.5t)=30}}}
{{{-60e^(-0.5t)=-30}}}
{{{e^(-0.5t)=1/2}}}
{{{-0.5t=ln(1/2)}}}
{{{t=-2*ln(1/2)}}}
{{{t=-2*(-0.693)}}}
{{{t=1.386}}}seconds
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Now find {{{v(1.386)}}}. 
{{{v(t)=-5+30e^(-0.5t)}}}
I'll leave that to you to finish.
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f) Blinky needed to be at a distance of greater than 60m.