Question

(a) Variation of acceIUL
(b) Variation of velocity with time.
(c) Variation of distance with time
Example 3.6 Galileo's law of odd
numbers: "The distances traversed, during
equal intervals of time, by a body falling
from rest, stand to one another in the same
ratio as the odd numbers beginning with
unity [namely, 1: 3: 5: 7......)." Prove it..
Answer Let us divide the time interval of
motion of an object under free fall into many
equal intervals t and find out the distances​

Answer 1

.

The distance traversed in nth second by a freely falling body is given by:

s

n

=0+

2

8

(2n−1) (initial velocity =0)

⇒s=

2

8

(2n−1)

So s is directly proportional to (2n−1) where n=1,2,3....

So in consecutive seconds of 1s,2s,3s and so on

Distance will vary as: 1m,(2×2−1)m,(2×3−1)m and so on

So s varies as: 1m,3m,5m,.