Question

A particle starts with some initial velocity and covers $x_1$ distance with $a_1$ acceleration and further $x_2$ distance with $a_2$ acceleration. If the final velocity is same as initial velocity then

• A. $a_1=-a_2$
• B. $a_1{x}_2=a_2{x}_1$
• C. $a_1{x}_1+a_2{x}_2=0$
• D. $\frac{a_1}{x_1}+\frac{a_2}{x_2}=0$

Answer 1

The correct option is C $a_1{x}_1+a_2{x}_2=0$


Let the initial velocity be $v_o$
For $x_1,v^2=u^2+2as$
$\Rightarrow v_1^2=v_o^2+2a_1{x}_1\left(1\right)$
and for $x_2,v^2=u^2+2as$
$v_o^2=v_1^2+2a_2{x}_2\left(2\right)$
From (1) and (2),
$\Rightarrow a_1{x}_1+a_2{x}_2=0$