(a) If x0 be the initial distance between nose of the rabbit and carrot, then distance between them after first, second, third, fourth,....
Second will be, x0/2, x0/4,x9/8, x0/16.......respectively.
Thus, the distance left, after n second.
x = x0 (1/2 + 1/22 +1/23 +1/24 +......)
or, x = x0e-At.
Putting the initial values,
x = x0/2 and t = 1, we get
x0/2 = x0 A-A or, = loge (2) = 0.693.
The position of the rabbit with respect to carrot at any time t, will be given as
x = x0e0.693t
For reaching x = 0, 0 = x = x0e-0.693t
⇒ t = ∝
It meant rabbit will never reach the carrot.
(b) The average velocity = distance travelled/time taken = x0/α = 0
The limiting value of average velocity is zero.
