Question 347061
v=30e^-t/2 -5
where t is the number of seconds after the brakes were applied.Assume the truck held its line under braking conditions.
1.calculate how long it took the truck to come to a stop. Express your answer as both an exact value and accurate to 2 decimal places.
{{{v=30e^(-t/2) -5 = 0}}}
{{{30e^(-t/2) = 5}}}
{{{e^(-t/2) = 1/6}}}
-t/2 = ln(1/6)
t = -ln(1/6)/2
t =~ 0.90 seconds
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2. At what time after braking was the truck's velocity 15m/s.Express your answer as both an exact value and accurate to 2 decimal places.
{{{v=30e^(-t/2) -5 = 15}}}
{{{30e^(-t/2) = 20}}}
{{{e^(-t/2) = 2/3}}}
-t/2 = ln(2/3)
t = -ln(2/3)/2
t =~ 0.20 seconds