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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Math

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justaguide's profile pic

Posted on

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.

pramodpandey's profile pic

Posted on

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

 

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