Answer
$s(t)=525t+25t^{2}$
Work Step by Step
Speed is the magnitude of velocity.
We equate speed and velocity as there is no change in direction of motion during the flight.
Adding the tail wind speed to the velocity of $500$ mph,
$v(t)=500+(25+50t)=525+50t$
Velocity is the derivative of position, so position is an antiderivative of velocity.
$s(t)=\displaystyle \int 525+50t=525t+50\cdot\frac{t^{2}}{2}$
$s(t)=525t+25t^{2}$
