An object with mass 500 g moves along x-axis with speed $v = 4\sqrt{x}$ m/s. The force acting on the object is :
Solution
<p>To find the force acting on the object, we use the formula $ F = m \times a $, where $ F $ is the force, $ m $ is the mass, and $ a $ is the acceleration.</p>
<p><p>The velocity $ v $ is given as $ v = 4 \sqrt{x} $.</p></p>
<p><p>Squaring both sides, we have $ v^2 = 16x $.</p></p>
<p><p>Differentiate $ v^2 $ with respect to $ x $: </p>
<p>$ 2v \frac{dv}{dx} = 16 $</p></p>
<p><p>Solving for $ \frac{dv}{dx} $, we find:</p>
<p>$ \frac{v \, dv}{dx} = \frac{16}{2} = 8 $</p></p>
<p><p>The force $ F $ is then calculated as:</p>
<p>$ F = 0.5 \times 8 = 4 \, \text{N} $</p></p>
<p>Thus, the force acting on the object is 4 N.</p>
About this question
Subject: Physics · Chapter: Laws of Motion · Topic: Newton's First Law
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