First slide
Instantaneous acceleration
Question

A body A starts from rest with an acceleration a1. After 2 second, another body B starts from rest with an acceleration a2. If they travel equal distances in the 5th second, after the start of A, then ratio a1 : a2 is equal to

Moderate
Solution

The distance covered by the first body A in 5th second after its start is given by
s5=u+a122t11=0+a12[(2×51)]or s5=9a12....(1)
The time taken by body B is given by t2 =5-2 =3 second
So, the distance covered by the second body in 3rd second after its start is given by
s3=u+a222t21=0+a22[(2×31)] or s3=5a22.....(2)
Given that
s5=s3 or 9a12=5a22
a1a2=59 or a1:a2=5:9

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