An object, moving with a speed of 6.25 m / s, is decelerated at a rate given by (d v/d t)=-2.5 √v where v is the instantaneous speed. The time taken by the object, to come to rest, would be

Question

An object, moving with a speed of 6.25 m / s, is decelerated at a rate given by (d v/d t)=-2.5 √v where v is the instantaneous speed. The time taken by the object, to come to rest, would be (A) 8 s (B) 1 s (C) 2 s (D) 4 s

Tardigrade Admin · Accepted Answer

∫ limitsv0 (d v/√v)=-∫ limits0t 2.5 d t 2 √v=2.5 t 2 √6.25=2.5 t t=2 s

Q. An object, moving with a speed of $6.25 m / s$ , is decelerated at a rate given by
$\frac{d v}{d t} = - 2.5 v$
where $v$ is the instantaneous speed. The time taken by the object, to come to rest, would be

$8 s$

$1 s$

$2 s$

$4 s$

$v \int 0 \frac{d v}{v} = - 0 \int t 2.5 d t$
$2 v = 2.5 t$
$2 6.25 = 2.5 t$
$t = 2 s$

Q. An object, moving with a speed of 6.25m/s, is decelerated at a rate given by dtdv​=−2.5v​ where v is the instantaneous speed. The time taken by the object, to come to rest, would be

8s

1s

2s

4s