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4-1.Newton's Laws of Motion
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A particle of mass $1\,kg$ is moving along $x-$ axis, where its velocity depends on $x-$ coordinate as $v = 2\sqrt x \,(m/s)$. Find the net force acting on the particle $2\,second$ after the start of motion ............ $N$
A
$1$
B
$2$
C
$4$
D
$\frac{3}{2}$
Solution
$\mathrm{v}=2 \sqrt{\mathrm{x}}=2 \mathrm{x}^{1 / 2}$
$\frac{d v}{d x}=\frac{1}{\sqrt{x}}$
acceleration $=\frac{\mathrm{dv}}{\mathrm{dt}}=\frac{\mathrm{dv}}{\mathrm{dx}} \cdot \frac{\mathrm{dx}}{\mathrm{dt}}$
$=\mathrm{v} \frac{\mathrm{dv}}{\mathrm{dx}}=2 \sqrt{\mathrm{x}} \cdot \frac{1}{\sqrt{\mathrm{x}}}=2 \mathrm{m} / \mathrm{s}^{2}$
Which is constant. Hence Net force at any
instant will be $\mathrm{F}=\mathrm{ma}=1 \times 2=2 \mathrm{N}$
Standard 11
Physics
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