Calculate the deceleration at each time step. Newton's second law states that the acceleration (deceleration is negative acceleration) is proportional to the force acting on it. Use this law, expressed in equation form as shown below, to calculate the deceleration (a) with the deceleration force (F) from the given curve and the known object mass (m).
a = F/m
Remember that deceleration is negative acceleration so the answer must have a negative sign.
Calculate the distance traveled in each time step. Using the following kinematic equation, calculate the distance traveled in each time step (s) using the size of the time step (t), the deceleration (a) calculated in Step 1, and the initial velocity of the object (v).
s = v*t+0.5*a*t^2
Calculate the energy at each time step. The energy (E) will be in the form of work, which is defined as some force acting over a certain distance. Use the deceleration force (F) from the given curve along with the distance calculated in Step 2 to calculate the energy according to the following equation:
E = F*s
Add the energy for each time step to get the total energy.