JEE Main 2025 Apr 7 Shift 2, Physics Q19: Newton's Laws Of Motion

JEE Main2025Apr 7, Shift 2Physics

An object with mass 500 g moves along x-axis with speed $v = 4 x$ m/s. The force acting on the object is :

Solution

Squaring the given velocity relation: $v^{2} = 16 x$ .

Using the kinematic identity $v \frac{d v}{d x} = a$ , differentiate implicitly: $2 v \frac{d v}{d x} = 16 \Rightarrow v \frac{d v}{d x} = 8$ .

So the acceleration is constant, $a = 8$ m/s $^{2}$ , and by Newton's second law $F = ma = 0.5 \times 8 = 4$ N.

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