Grade 12th passMechanics
a body falls freely from rest covers more distances in each next second .these distances are in ratio?
2 Answers
Khimraj
Distance traveled in each nth sec is given bySn = (1/2)g(2n-1)So the ratio of distance in 1st sec 2nd sec 3 sec and so on is given by1:3:5:7:9...
Nikhil Sukhani
Let u = initial speed
t = time taken
a = acc.
then ,
distance covered in n seconds (S1) = u(n) +1/2a(n)2
= nu + 1/2an2
distance covered in n-1 seconds (S2) = u(n-1) +1/2a(n-1)2
= nu - u + 1/2an2 +1/2a - an
distance vovered in nth second = Sn – Sn-1
= nu +1/2an2 - ( nu - u +1/2an2 +1/2a – an )
= u – 1/2a +an
= u -a(1/2-n)
= u + a/2(2n-1)
Since body falls freely from rest
Therefore , a=g
u=0
So , the formula becomes g/2(2n-1)
So the ratio of distance travelled in 1st sec , 2nd sec 3rd sec.... is 1:3:5:...
CHEERS ;)
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