Question

A 15kg mass accelerated from rest with a force of 100N. as it moves faster,friction and air resistance create an oppositely directed retarding force given F=A+BV. Where A=25N and B=0.5Ns/m. At what velocity does the acceleration equal to one half of the initial acceleration

Answer 1

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,

⇒ 5/2 = (100 - 25 - 0.5v)/15

⇒ 75 = 200 - 50 - v

⇒ 75 = 150 - v

⇒ v = 150 - 75

∴ v = 75 m/s.