Question

$\begin{array}{c}\text{A}15kg\text{mass is accelerated from rest with a force of}100N\text{. As it moves friction and air resistance}\\ \text{create an oppositely directed retarding force given by}{F}_R=A+BV\text{. where}A=25N\text{and}B=0.5\frac{N}{m/s}\text{.}\\ \text{Atwhat velocity does the acceleration equal to one half of the initial acceleration?}\end{array}$

• A. $25{ms}^{-1}$
• B. $50{ms}^{-1}$
• C. $75{ms}^{-1}$
• D. $100{ms}^{-1}$

Answer 1

The correct option is C $75{ms}^{-1}$

Mass of the body $=15kg.$

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

$Force=100N.$

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$].$

$\Rightarrow 15a=75$

$\therefore a=5m/s².$

Now$,$ According to the question$,$

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

$\Rightarrow 5/2=(100-25-0.5v)/15$

$\Rightarrow 75=200-50-v$

$\Rightarrow 75=150-v$

$\Rightarrow v=150-75$

$\therefore v=75m/s.$

Hence,

option $\left(C\right)$ is correct answer.