Three quick physics calculators: the energy of a moving object, the energy stored by lifting something, and the power needed to do an amount of work in a given time.
Kinetic energy is the energy of motion: KE = ½ × mass × speed². Because speed is squared, doubling your speed quadruples the energy. A 1,500 kg car at 50 km/h (13.9 m/s) carries about 145 kJ; at 100 km/h that becomes about 579 kJ, which is why braking distances grow so quickly.
Gravitational potential energy is the energy stored by lifting something: PE = m × g × h. Lifting a 70 kg person 10 m stores 70 × 9.81 × 10 ≈ 6,867 J. Released, that energy turns back into motion, reaching √(2gh) ≈ 14 m/s at the bottom.
Power is how fast work is done: P = W ÷ t. Climbing those 10 m in 12 seconds takes about 572 W, or 0.77 horsepower. One mechanical horsepower is 745.7 W.
KE = ½mv², with mass in kilograms and speed in metres per second, giving joules. A 2 kg ball at 3 m/s has ½ × 2 × 9 = 9 J.
Gravitational PE = mgh: mass (kg) × gravity (9.81 m/s² on Earth) × height (m), in joules. It is measured relative to whatever height you choose as zero.
Because speed is squared in ½mv². Going from 50 to 100 km/h multiplies the energy by 2² = 4, which is why crashes at higher speeds are so much more severe.
The SI unit of energy: the work done by a force of 1 newton over 1 metre. One kilocalorie (food Calorie) is 4,184 J and one watt-hour is 3,600 J.
Divide by 745.7 for mechanical (imperial) horsepower. 1 kW ≈ 1.34 hp.
