Any familiarity with the concept of kinetic energy will make it clear to you that since K.E. is based on the mass and velocity of an object, objects with greater mass or higher velocities will have greater kinetic energy values.
Mathematically, Kinetic energy is represented by the formula,
K.E=1/2mv2
Where K.E is Kinetic Energy, m is equal to mass and v is velocity/speed.
To prove the claim mathematically, we can take two objects with different masses and velocities.
O1 is an object with a mass equal to 10 grams and is moving with a velocity/speed of 100 m/s (meters per second), while O2 is an object with a mass of 100 grams and a velocity/speed of 1000 m/s.
Let’s calculate the kinetic energy for both objects O1 and O2 using the formula.
Putting the data in the formula to calculate the Kinetic energy of O1,
- Mass m1=10 grams (convert to kilograms:
m1=10 grams×10001=0.01 kg=10grams×10001=0.01kg) - Velocity v1=100 m/s
K.E.1 = 1/2×0.01kg×(100m/s)2
K.E.1= 1/2×0.01 kg×10000 m2/s2
K.E.1= 0.5×100 kg⋅m2/s2
K.E.1=50 joules
Putting the data in the formula to calculate the Kinetic energy of O2,
K.E.2 = 1/2×0. 1kg×(1000m/s)2
K.E.2= 1/2×0.1 kg×1000000 m2/s2
K.E.2= 0.5×100000 kg⋅m2/s2
K.E.2=50000 joules
From the given calculation, it is proven that the body possessing greater mass and speed will always have the most kinetic energy.