19.
Each second a rabbit moves half the remaining distance from his nose to the
head of a lettuce. Does he ever get to the lettuce? What is the limiting value of
his average velocity? Draw graphs showing his velocity and position as time
increases.
Answers
Answer:
Yes, the rabbit will get to the lettuce. To understand it better, let us assume that initially, the distance between the rabbit and the lettuce (x) is s . Therefore the distance traveled by the rabbit in 1st second is s/2 . The remaining distance to the lettuce s/2 is and the distance traveled by the rabbit now will be exactly one-half this value i.e. s/4 .
Therefore, the distance between the rabbit and lettuce falls every second as:
x = s \ (at \ t = 0\ sec), x = \frac{s}{2} (at\ t\ = \1\sec), x = \frac{s}{4} , x = \frac{x}{4} (at \ t = \3 \ sec)............
After some time, the distance between the rabbit and the lettuce will be so small that the rabbit will almost reach its destination. The limiting value in this case will occur for the change in distance\Delta x \rightarrow 0 .
Explanation:
thankyou.
Answer:
Explanation: To understand it better, let us assume that initially, the distance between the rabbit and the lettuce (x) is s . Therefore the distance traveled by the rabbit in 1st second is s/2 . The remaining distance to the lettuce s/2 is and the distance traveled by the rabbit now will be exactly one-half this value i.e. s/4 .
Therefore, the distance between the rabbit and lettuce falls every second as:
x = s \ (at \ t = 0\ sec), x = \frac{s}{2} (at\ t\ = \1\sec), x = \frac{s}{4} , x = \frac{x}{4} (at \ t = \3 \ sec)............
After some time, the distance between the rabbit and the lettuce will be so small that the rabbit will almost reach its destination. The limiting value in this case will occur for the change in distance\Delta x \rightarrow 0 .
The table below shows the limiting process, in which the initial point x1 (m) of the rabbit (measured from the starting point) tends to reach the final point x2 (m) (measured from starting point), over each time interval of 1
Therefore the limiting value of average velocity will be closer to s /128 for a particular value of s .
It is important to note that the value of initial point in the table above is measured from the starting point. After one second, the rabbit has travelled distance s/2 , therefore he is that much distance away from the initial point. After another second, the rabbit has travelled a distance of s / 4 , therefore the rabbit s/2 +s/4 is meters away from the starting point i.e. 3s/4. This is repeated for every second and the limiting condition is approached.
The position (x) of the rabbit from the starting point after t seconds is given as:
x = s-s \left ( \frac{1}{2} \right )^{t}
One can match the value x1 (m) of in the table above with the values of (x) for . t = 1,2,3....
The graph below shows the position of rabbit from the starting position after t seconds:
