Each second a rabbit moves half the remaining distance from his nose t

1.	Each second a rabbit moves half the remaining distance from his nose to a carrot. (a) Does he ever get to the carrot?(b) What is the limiting value of his average velocity?
Answer» (a) If x₀be 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 = x₀e^0.693t 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.

Each second a rabbit moves half the remaining distance from his nose to a carrot. (a) Does he ever get to the carrot?(b) What is the limiting value of his average velocity?

Answer»

(a) If x₀be 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 = x₀e^0.693t

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.