Question

A particle moves for 8 seconds if first accelerates from rest and then retards to rest if the retardation be three times the acceleration then time for which it accelerates will be

Answer 1

Let the time for which it accelerates be t
Then the time for retardation will be 8-t
Let the velocity after acceleration be v1
Let the acceleration be a
From Newton's first eq. of motion
v1=u+at
Here u=0(it starts from rest)
v1=at ......1st
Now retardation=3a(given)
Hence , v=v1-3a(8-t)
Here v=0(it again comes to rest)
v1=3a(8-t)
Putting v1 from 1st
at=3a(8-t)
t=3(8-t)
t=24-3t
4t=24
t=6seconds

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Answer 2

Question ⬇

A particle moves for 8 seconds if first accelerates from rest and then retards to rest if the retardation be three times the acceleration then time for which it accelerates will be

ANSWER⬇

Let 't' be time of acceleration

Then retardation time =θ−t total time = 8 sec

[D]  Let V  1  be velocity after acceleration  

let acceleration be a

V1=u+at

here u=0

V1  =at→(i)

none retardation = 3a (given)

Hence,

Hence,V=V1

Hence,V=V1−3a(8−t)

V=0,

V1=3a(8−t)

at=3a(8−t)

,putV  1

 from(i)

             t=24−3t

           4t=24

           t=6second

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