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

The correct answer is Option 2. Full mathematical solution steps and hints are accessible in the interactive StemCET workspace.

Physics Q28 – JEE-MAIN 2025

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Home Physics Laws of MotionQuestion #230

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 :

Clue 1 of 3: Conceptual Principle

To find the force, you need to relate mass and acceleration using Newton's Second Law.

🧠 Full Solution Path

Step 1: Convert Mass and Identify Given Information✦ Active

The mass of the object is given as $m = 500 g$ . Convert this to kilograms:

m = 500 g = 0.5 kg

The speed of the object is given as a function of position $x$ :

v = 4 \sqrt{x} = 4 x^{1 / 2} m/s

Step 2: Calculate Acceleration○ Expand

Since velocity $v$ is a function of position $x$ , we use the chain rule to find acceleration $a = \frac{d v}{d t} = \frac{d v}{d x} \frac{d x}{d t} = v \frac{d v}{d x}$ . First, find $\frac{d v}{d x}$ :

\frac{d v}{d x} = \frac{d}{d x} (4 x^{1 / 2}) = 4 \cdot \frac{1}{2} x^{(1 / 2 - 1)} = 2 x^{- 1 / 2} = \frac{2}{\sqrt{x}}

Now, substitute $v$ and $\frac{d v}{d x}$ into the acceleration formula:

a = v \frac{d v}{d x} = (4 \sqrt{x}) (\frac{2}{\sqrt{x}}) = 4 \cdot 2 = 8 {m/s}^{2}

💡 Teacher's Secret Hint

Remember to use the correct form of acceleration when velocity is given as a function of position, not time.

Step 3: Calculate Force○ Expand

Using Newton's Second Law, $F = m a$ :

F = (0.5 kg) (8 {m/s}^{2}) = 4 N

💡 Teacher's Secret Hint

Ensure all units are in SI (kilograms, meters, seconds) before calculating force in Newtons.

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Physics Question 28 – JEE-MAIN 2025

Clue 1 of 3: Conceptual Principle

🧠 Full Solution Path