Understanding the Concepts
* Work-Energy Theorem: The work done on an object is equal to the change in its kinetic energy.
* Kinetic Energy: The energy an object possesses due to its motion, calculated as KE = (1/2)mv², where m is mass and v is velocity.
Derivation
1. Initial Kinetic Energy (KE₁): (1/2)mv²
2. Final Kinetic Energy (KE₂): (1/2)m(2v)² = 2mv²
3. Change in Kinetic Energy (ΔKE): KE₂ - KE₁ = 2mv² - (1/2)mv² = (3/2)mv²
4. Work (W): According to the work-energy theorem, W = ΔKE = (3/2)mv²
Answer
The work required to accelerate an object on a frictionless surface from speed *v* to *2v* is (3/2)mv².
