Question

Freddi Fish-(TM) has a position as a function of time given by x = a/(b + t^2). (a) Infer the units of the constants a and b. (b) Find her maximum speed, (c) Check that your answer has the right units.

Answer 1

Given
  
Freddi fish position as a function of time

x= a/(b+t^2)

can be written as

x = a/b + a/t^2

a)

x is position of the fish , units are meters

so

the units of a ,b are

   a ---- m.s^2
  
   b ----- s^2

the time derivative of displacement is velocity

   dx/dt = (d/dt)(a/b+ a/t^2)

   = -2a t^-3 m/s

      
c)checking units

   a -- --- ms^2

   t^-3 ----- s^-3

   m s^2*s^-3 = m/s