Question

The law of motion of a body moving along a straight line is $x=\frac{1}{2}vt$, $x$ being its distance from a fixed point on the line at time $t$ and $v$ is its velocity there. Then

• A. acceleration $f$ varies directly with $x$
• B. acceleration $f$ varies inversely with $x$
• C. acceleration $f$ is constant
• D. acceleration $f$ varies directly with $t$

Answer 1

Answer: (A)

acceleration $f$ varies directly with $x$

$2x=vt$
$\Rightarrow 2\frac{dx}{dt}=v+tf$
$\Rightarrow 2v=v+ft\Rightarrow v=tf$
$\Rightarrow f=\frac{v}{t}\Rightarrow f=\frac{2x}{t^2}$
$\Rightarrow f\propto x$