Question

A shelter Island ferry boat moves with a cosntant velocity vox =8 m/sfor 60 sec.It then shuts off its engines and coasts.Its coasting velocity is given by vx = vox t21 /t2,

where t1= 60 s.What is the displacement of the boat for the interval 0<t<∞?

Answer 1

Displacement in 60 s:

$$\Delta x_1=v_{0x}T^2/T=480\text{ m}.$$

Displacement during the other interval of time:

$$\Delta x_2=\int^\infty_Tv_x\text dt=\\\space\\ =\int^\infty_T\frac{v_{0x}T^2}{t^2}\text dt=\\\space\\ =v_{0x}T^2\int^\infty_T\frac{1}{t^2}\text dt=\\\space\\ v_{0x}T^2(-1/t)|^\infty_T=480\text{ m}.$$

The total displacement is

$$\Delta x=\Delta x_1+\Delta x_2=960\text{ m}.$$