Question

The law of motion of a body moving along a straight line is \(x=\frac{1}{2} v t, x\) being its distance from a fixed point on the line at time \(t\) and \(v\) is its velocity there. Then
(A) acceleration \(\mathrm{f}\) varies directly with \(\mathrm{x}\)
(B) acceleration \(f\) varies inversely with \(x\)
(C) acceleration \(\mathrm{f}\) is constant
(D) acceleration \(\mathrm{f}\) varies directly with \(\mathrm{t}\)

Answer 1

Ans : (A)
Hint \(: x=\frac{1}{2} v t \Rightarrow \frac{d x}{d t}=\frac{1}{2}\left[v+t \frac{d v}{d t}\right] \Rightarrow v=\frac{v}{2}+\frac{1}{2} t f \Rightarrow f=\frac{v}{t} \Rightarrow f=\frac{2 x}{t^{2}}\)

Answer 2

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Answer 3

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