Enter the (constant) acceleration (m/s²), the time it is applied (s), and the mass (kg) into the calculator to estimate the kinetic energy gained starting from rest (assuming straight-line motion and no losses).
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Energy from Acceleration Formula
The following equation is used to calculate the kinetic energy gained from a constant acceleration applied over a time interval, assuming the object starts from rest (so that v = a·t).
E = \frac{1}{2} m (a t)^2- Where E is the kinetic energy gained (Joules, J)
- a is the (constant) acceleration magnitude (m/s²)
- t is the time the acceleration is applied (s)
- m is the mass (kg)
To calculate the energy from acceleration (starting from rest), first calculate the speed change v = a·t, then compute kinetic energy E = ½·m·v².
How to Calculate Energy from Acceleration?
The following example problems outline the steps and information needed to calculate the Energy from Acceleration.
Example Problem #1
- First, determine the acceleration (m/s²). In this example, the acceleration is 4.
- Next, determine the time (s). For this problem, the time is 5.
- Next, determine the mass (kg). In this case, the mass is 4.
- Finally, calculate the Energy from Acceleration using the formula above (starting from rest).
E = ½ · m · (a · t)²
Inserting the values from above and solving the equation yields:
E = 0.5 * 4 * (4 * 5)² = 0.5 * 4 * 20² = 800 (Joules)
Example Problem #2
Using the same method as above, first, we need to measure or determine the variables required by the equation. For this example problem, these are provided as follows:
acceleration (m/s²) = 6
time (s) = 8
mass (kg) = 3
Entering these given values into the calculator above yields:
E = 0.5 * 3 * (6 * 8)² = 0.5 * 3 * 48² = 3456 (Joules)
