JEE Main · 2005 · 08 May 2005 · Offline · Application of Derivatives

Two points

A

and

B

move from rest along a straight line with constant acceleration

f

and

f^{'}

respectively. If

A

takes

m

sec. more than

B

and describes '

n

' units more than

B

in acquiring the same speed then

Answer: (D)

Solution

Let

B

reach the common speed

v

in time

t

; then

A

, having the smaller acceleration, needs

t + m

. Equal final speeds require

f^{'} t = f (t + m)

, so

t = \frac{f m}{f ^{'} - f}

and

t + m = \frac{f ^{'} m}{f ^{'} - f}

. The extra distance is

n = \frac{1}{2} f (t + m)^{2} - \frac{1}{2} f^{'} t^{2} = \frac{f f ^{'} m ^{2}}{2 ( f ^{'} - f )}

, which rearranges to

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

JEE Main · 2005 · 08 May 2005 · Offline · Single correct option