# Calculating Velocity and Distance

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8. Ignoring resistance, a sailboat starting from rest accelerates at a rate proportional to the difference between the velocities of the wind and the boat.

(a) The wind is blowing at 20 knots, and after 1 half-hour the boat is moving at 10 knots. Write the velocity as a function of time .

(b) Use the result of part (a) to write the distance traveled by the boat as a function of time.

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#### Solution Preview

8. Ignoring resistance, a sailboat starting from rest accelerates at a rate proportional to the difference between the velocities of the wind and the boat.

Since it's proportional, then we have:

(dv_b)/dt=a(v_w-v_b )

Here a is a constant of proportionality. If the acceleration is directly proportional, then a =1, which is what we'll assume. vw and vb are the velocities of the wind and boat respectively.

(a) The wind is blowing at 20 knots, and after 1 half-hour the boat is moving at 10 knots. Write the velocity as a ...

#### Solution Summary

The expert calculates velocity and distance.