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 t^2(1 /t^2)
,
where t1= 60 s.What is the displacement of the boat for the interval 0<t<à ¢ ˆ ž?

Answer 1

Displacement during 60 s:

$$\Delta x_1=v_{0x}60^2/60^2=8\text{ m}.$$

Displacement during 0<t<∞:

$$\Delta x_2=\int^\infty_Tv_x\text dt=\\\space\\ =v_{0x}T^2\int^\infty_T\frac1{t^2}\text dt=480\text{ m}.\\\space\\ \Delta x=\Delta x_1+\Delta x_2=488\text{ m}.$$