Question

The position of a ship traveling due east along a straight line is s(t) = 12t2 + 6. 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?

Answer 1

18 miles east; 24 mph east

Step-by-step explanation:

In order to find how far east of Wilmington is the ship after 1 hour, we just need to substitute t = 1 into the formula of the position.

The equation of the position is

`s(t) = 12 t^2 +6`

where t is the time. Substituting t = 1,

`s(1) = 12 (1)^2 + 6 = 12+6 = 18 mi`

So, the ship is 18 miles east of Wilmington.

To find the velocity of the boat, we just need to calculate the derivative of the position, so

`v(t) = s'(t) = 24 t`

And by substituting t = 1, we find the velocity after 1 hour:

`v(1) = 24 (1) = 24 mph`

And the direction is east.