Which is the equation for an object’s kinetic energy?(1 point)%0D%0AResponses%0D%0A%0D%0AKE=12mv2%0D%0AUpper K Upper E equals Start Fraction 1 over 2 End Fraction m v squared%0D%0A%0D%0AKE=2mv2%0D%0AUpper K Upper E equals 2 m v squared%0D%0A%0D%0AKE=2m2v%0D%0AUpper K Upper E equals 2 m squared v%0D%0A%0D%0AKE=12m2v
The equation for an object's kinetic energy is:
KE = 1/2 mv^2
The correct equation for an object's kinetic energy is:
KE = 1/2mv^2
So, the correct option is:
Upper K Upper E equals Start Fraction 1 over 2 End Fraction m v squared
The equation for an object's kinetic energy is:
KE = ½mv²
Here's how you can understand and derive the equation:
1. Kinetic energy (KE) is the energy possessed by an object due to its motion. It depends on the mass (m) and velocity (v) of the object.
2. The formula for kinetic energy is based on the work-energy principle, which states that the work done on an object is equal to its change in kinetic energy.
3. Work (W) is defined as the force (F) applied to an object multiplied by the displacement (d) of the object in the direction of the applied force. Mathematically, it can be written as W = F × d.
4. When a constant force is applied to accelerate an object, the work done can be calculated using the equation W = ½mv², where m is the mass of the object and v is the final velocity.
5. Equating the work done to the change in kinetic energy, we have W = ΔKE.
6. Since ΔKE is the change in kinetic energy, we can rewrite it as ΔKE = KEf - KEi, where KEf is the final kinetic energy and KEi is the initial kinetic energy. In this case, the object starts from rest, so KEi = 0.
7. Therefore, ΔKE = KEf - 0 = KEf.
8. Equating W and ΔKE, we have ½mv² = KEf.
Hence, the equation for an object's kinetic energy is KE = ½mv².