# A defective airplane starts from rest and the speed of the airplane is given by s(t) = 15t^2 - 8t. What is the distance traveled by the aircraft in 12 seconds.

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The airplane starts from rest and its speed is given as a function of the time after takeoff (t) by `s(t) = 15t^2 - 8t` .

The distance (d) traveled by an object with speed (s) in time (t) is given by d = s*t. For the airplane s is a function of t, the distance traveled by the airplane in 12 seconds is given by the integral:

`int_0^12 s(t)* dt`

= `int_0^12 (15t^2 - 8t) dt`

= `(15t^3/3 - 8t^2/2)_0^12`

= `(5t^3 - 4t^2)_0^12 `

= `5*(12^3 - 0) - 4*(12^2 - 0)`

= 8640 - 576

= 8064

**The distance traveled by the airplane in 12 seconds after takeoff is 8064 units.**

Plane start from rest and speed at any moment of time t is given

Thus it will travel in 12 second

D=`int_0^12s(t)dt`

`=int_0^12(15t^2-8t)dt`

`=(5t^3-4t^2)_0^12`

`=144(60-4)`

`=8064` Unit