The position of a ship traveling due east along a straight line is s(t) = 16t2 + 8.

Question

The position of a ship traveling due east along a straight line is s(t) = 16t² + 8. In this example, time t is measured in hours and position s is measured in nautical miles. We will take s = 0 to be the port of Wilmington, NC, and the positive direction to be east. How far east of Wilmington is the ship and how fast is it going after one hour, that is, when t = 1?

After one hour, the ship is ___nautical miles east of Wilmington, with an instantaneous speed of  ___knots (nautical miles per hour).

I know the ship is 24 miles east of Wilmington. But I do not think the instantaneous speed should also be 24 miles. How do I get the instantaneous speed of this question?

Answer 1

s(t) =16t^2 + 8

instantaneous speed = v(t) = s'(t) = 32t

s'(1) = 32(1) = 32 knots