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JEE Main 2005

Exam: JEE Main
Year: 2005
Subject: Physics
Chapter: Motion in One Dimension

JEE Main 2005 · Physics · Motion in One Dimension

Two points A and B move from rest along a straight line with...

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

Options

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

Correct answer

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

Step-by-step solution

\begin{aligned}& v²=2 f(d+n)=2 f^{\prime} d \\ & v=f^{\prime}(t)=(m+t) f \end{aligned}

eliminate

d and m

we get

\left(f^{\prime}-f\right) n=\frac{1}{2}f f^{\prime} m² \text{. }

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