Question

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? _________________________

Answer 1

At t=2s the car reach its minimum speed

Minimum speed=8m/s

Explanation:

We are given that velocity of car

`v(t)=t^2-4t+12`

0<t<4

Differentiate w.r.t t

`v'(t)=2t-4`

`v'(t)=0`

`2t-4=0`

`2t=4`

`t=2`

`v''(t)=2>0`

The velocity is minimum at t=2 s

Substitute t=2

`v(2)=2^2-4(2)+12`

`v(2)=8m/s`

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