A particle moves for 50 seconds if first accelerates from rest and then retard or deaccelerates to rest. If the retardation be 5 times the acceleration then the time for retardation is:

Question

A particle moves for 50 seconds if first accelerates from rest and then retard or deaccelerates to rest. If the retardation be 5 times the acceleration then the time for retardation is: (A) 25 / 3 second (B) 50 / 3 second (C) 25 second (D) 100 / 3 second

Tardigrade Admin · Accepted Answer

Let particle accelerates with acceleration

α

for time

t_{1},

and retard with retardation

- β

for

t_{2}

t_{1} + t_{2} = 50

CASE -1	CASE -2
$v = u + α t_{1}$	$v = u - β t_{2}$
$v = 0 + α t_{1}$	$0 = u - β t_{2}$
$v = α t_{1}$	$u = β t_{2}$

Initial velocity is equal to the final velocity of

C a se I .

α t_{1} = β t_{2}

α t_{1} = 5 α t_{2}

α t_{1} = 5 α t_{2} \Rightarrow 5 t_{2} + t_{2} = 50

6 t_{2} = 50 \Rightarrow t_{2} = 25/3 sec

Q. A particle moves for $50$ seconds if first accelerates from rest and then retard or deaccelerates to rest. If the retardation be $5$ times the acceleration then the time for retardation is:

$25/3$ second

$50/3$ second

25 second

$100/3$ second

Q. A particle moves for 50 seconds if first accelerates from rest and then retard or deaccelerates to rest. If the retardation be 5 times the acceleration then the time for retardation is:

25/3 second

50/3 second

25 second

100/3 second

Q. A particle moves for $50$ seconds if first accelerates from rest and then retard or deaccelerates to rest. If the retardation be $5$ times the acceleration then the time for retardation is:

$25/3$ second

$50/3$ second

$100/3$ second