An object with mass 500 g moves along x-axis with speed v = 4√x m/s. The force acting on the object is:
❓ Question An object with mass 500 g moves along the x-axis with speed v = 4 x m/s . The force acting on the object is: ? 🖼️ Question Image ✍️ Short Solution We are given velocity as a function of position , v ( x ) = 4 x v(x) = 4\sqrt{x} , and mass m = 0.5 kg m = 0.5\ \text{kg} . To find the force , recall Newton’s Second Law : F = m d v d t . Since velocity is a function of position, apply chain rule : d v d t = d v d x ⋅ d x d t = v d v d x . Hence, F = m v d v d x . 🔹 Step 1: Compute dv/dx v = 4 x ⟹ d v d x = 4 ⋅ 1 2 x − 1 / 2 = 2 x . 🔹 Step 2: Substitute values F = m ⋅ v ⋅ d v d x = 0.5 ⋅ ( 4 x ) ⋅ 2 x . Simplify: F = 0.5 ⋅ 4 ⋅ 2 = 4 N . 🧮 Image Solution ✅ Conclusion & Video Solution ✅ Answer: F = 4 N 📘 Concept Recap: When velocity is given as a function of position, force can be computed using F = m v d v d x . Here, even though v v v increases with x x x , the resulting force is constant . This implies uni...