Question

Two points $A$ and $B$ move from rest along a straight line with same acceleration $f$ and $f^{\prime }$ respectively. If $A$ takes $m\text{sec}$ more than $B$ and describes $n$ units more than $B$ in acquiring the same speed then

• A. $(f-f^{\prime })m^2=f{f}^{\prime }n$
• B. $(f+f^{\prime })m^2=f{f}^{\prime }n$
• C. $\frac{1}{2}(f+f^{\prime })m=f{f}^{\prime }{n}^2$
• D. $(f^{{}^{\prime }}-f)n=\frac{1}{2}f{f}^{{}^{\prime }}{m}^2$

Answer 1

Answer: (D)

$(f^{{}^{\prime }}-f)n=\frac{1}{2}f{f}^{{}^{\prime }}{m}^2$

$v^2=2f(d+n)=2f^{\prime }d$

$v=f^{\prime }\left(t\right)=(m+t)f$

eliminate $d$ and $m$ we get $(f^{{}^{\prime }}-f)n=\frac{1}{2}f{f}^{{}^{\prime }}{m}^2$