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1. The velocity of a car as it travels over a level crossing is modeled by v = t2 – 4t + 12

for 0 < t < 4 where t is the time in seconds after it reaches the crossing. When does the car reach its minimum speed? What is the minimum speed?


Show your work or strategy:





When does the car reach its minimum speed? _________________





What is the minimum speed? _________________________

Respuesta :

lublana

Answer:

At t=2s the car  reach its minimum speed

Minimum speed=8m/s

Step-by-step explanation:

We are given that velocity of car

[tex]v(t)=t^2-4t+12[/tex]

0<t<4

Differentiate w.r.t t

[tex]v'(t)=2t-4[/tex]

[tex]v'(t)=0[/tex]

[tex]2t-4=0[/tex]

[tex]2t=4[/tex]

[tex]t=2[/tex]

[tex]v''(t)=2>0[/tex]

The velocity is minimum at t=2 s

Substitute t=2

[tex]v(2)=2^2-4(2)+12[/tex]

[tex]v(2)=8m/s[/tex]

Hence, the speed of car is minimum at t=2 se and minimum speed of car=8m/s

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