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