Enter the mass and the speed into the calculator to determine the work required to accelerate an object from rest to that speed (this equals the object’s kinetic energy at that speed).
Work From Velocity Formula
The following formula is used to calculate the work required to accelerate an object from rest to a speed v (this equals the kinetic energy at that speed).
W = 1/2*m*v^2
- Where W is the work (J)
- m is the mass (kg)
- v is the speed (m/s)
To calculate the work to accelerate from rest to a speed v, multiply the mass by the speed squared, then divide by 2. (More generally, the net work done equals the change in kinetic energy: W = 1/2·m·(v22 − v12)).
| Speed (m/s) | Work (J) | ft⋅lb | kJ | cal |
|---|---|---|---|---|
| 0.5 | 0.125 | 0.092 | 0.000 | 0.030 |
| 1 | 0.500 | 0.369 | 0.001 | 0.120 |
| 1.5 | 1.125 | 0.830 | 0.001 | 0.269 |
| 2 | 2.000 | 1.475 | 0.002 | 0.478 |
| 2.5 | 3.125 | 2.305 | 0.003 | 0.747 |
| 3 | 4.500 | 3.318 | 0.005 | 1.076 |
| 4 | 8.000 | 5.900 | 0.008 | 1.912 |
| 5 | 12.500 | 9.220 | 0.013 | 2.988 |
| 6 | 18.000 | 13.276 | 0.018 | 4.302 |
| 7.5 | 28.125 | 20.744 | 0.028 | 6.722 |
| 8 | 32.000 | 23.602 | 0.032 | 7.648 |
| 9 | 40.500 | 29.871 | 0.041 | 9.680 |
| 10 | 50.000 | 36.878 | 0.050 | 11.950 |
| 12 | 72.000 | 53.104 | 0.072 | 17.208 |
| 15 | 112.500 | 82.976 | 0.113 | 26.888 |
| 18 | 162.000 | 119.485 | 0.162 | 38.719 |
| 20 | 200.000 | 147.512 | 0.200 | 47.801 |
| 25 | 312.500 | 230.488 | 0.313 | 74.689 |
| 30 | 450.000 | 331.903 | 0.450 | 107.553 |
| 40 | 800.000 | 590.050 | 0.800 | 191.205 |
| Assumes mass m = 1.00 kg and the object starts from rest. Formula: W = 0.5 × m × v². Unit refs: 1 ft⋅lb = 1.35582 J; 1 J = 0.737562 ft⋅lb = 0.239006 cal; 1 kJ = 1000 J. | ||||
How to Calculate Work From Velocity?
The following example problem outlines how to calculate the work required to accelerate an object from rest to a given speed.
Example Problem #1:
- First, determine the mass (kg). In this example, the mass (kg) is given as 81.
- Next, determine the speed (m/s). For this problem, the speed (m/s) is given as 58.
- Finally, calculate the work using the equation above:
W = 1/2*m*v^2
Inserting the values from above and solving the equation with the input values gives:
W = 1/2*81*58^2= 136,242 (J)
FAQ
What is the significance of the “Work From Velocity” formula in physics?
This formula (in the form W = 1/2·m·v²) gives the work required to accelerate an object from rest to speed v, which is equal to the object’s kinetic energy at that speed. More generally, the work–energy theorem states that the net work done on an object equals the change in kinetic energy: Wnet = ΔK = 1/2·m·(v22 − v12).
How does mass affect the work done from velocity?
For a given speed v, the work to accelerate from rest is proportional to mass: W = 1/2·m·v². Doubling the mass doubles the required work for the same final speed.
Can the “Work From Velocity” formula be applied to all types of motion?
The specific form W = 1/2·m·v² applies to translational motion starting from rest (or as a kinetic energy calculation at speed v). For a general change in speed from v1 to v2, use W = 1/2·m·(v22 − v12). The work–energy theorem holds even when forces vary with time or position; constant force is not required. For rotational motion, analogous relationships use rotational kinetic energy (e.g., 1/2·I·ω²).
