Question

A 15 kg mass is accelerated from rest with a force of 100n.as it moves faster,friction and air resistance create an oppositely directed retarding force given by FR=A+BV. Where A=25N and B=0.5Ns/m. At what velocity does the acceleration becomes equal to one half of the initial acceleration.<br /><br />1)25m/s 2)50m/s3)75m/s 4)100m/s

Answer 1

Answer ⇒ Option (c). 75 m/s.

Mass of the body = 15 kg.

Initial velocity = 0 [since, the body is accelerated from the rest position].

Force = 100 N.

Refers to the attachment for the question.

In the Attachment it is clearly shown,  

100 - (A + Bv) = 15a

where, a is the acceleration.

100 - (25 + 0) = 15a    [Since, v is at rest initially].

⇒ 15a = 75

∴ a = 5 m/s².

Now, According to the question,

$\frac{5}{2}  = \frac{100 - (A + Bv)}{15}$

⇒ 5/2 = (100 - 25 - 0.5v)/15

⇒ 75 = 200 - 50 - v

⇒ 75 = 150 - v

⇒ v = 150 - 75

∴ v = 75 m/s.

Hence, the velocity of the body is 75 m/s.

Option (c). is correct.

Hope it helps.