Given:
- Initial kinetic energy (Ei) = 0 J (object is at rest initially)
- Final kinetic energy (Ef) = 400 J
- Time (t) = 2 seconds

To Find:
- Mass of the object

Formula:
- Kinetic energy (K) = 0.5 * mass (m) * velocity (v)^2

Explanation:

We can use the formula for kinetic energy to calculate the mass of the object. Since the object starts from rest, the initial kinetic energy is zero.

At the end of 2 seconds, the object possesses 400 J of kinetic energy. We can equate this to the final kinetic energy equation:

Ef = 0.5 * m * v^2

Since the object falls vertically downwards, the only force acting on it is gravity. The acceleration due to gravity is approximately 9.8 m/s^2.

Step 1: Calculate the final velocity (v) using the equation of motion:

v = u + at

Here, initial velocity (u) is 0 m/s and acceleration (a) is 9.8 m/s^2.

v = 0 + 9.8 * 2
v = 19.6 m/s

Step 2: Substitute the values of Ef and v into the kinetic energy equation and solve for the mass (m):

400 = 0.5 * m * (19.6)^2
400 = 0.5 * m * 384.16
400 = 192.08m
m = 400 / 192.08
m ≈ 2.08 kg

Therefore, the mass of the object is approximately 2.08 kg.

Summary:
- The object falls from rest and possesses 400 J of kinetic energy at the end of 2 seconds.
- Using the equation for kinetic energy, we can calculate the mass of the object.
- By applying the equation of motion and substituting the values, we find the final velocity to be 19.6 m/s.
- Substituting the values of Ef, m, and v into the kinetic energy equation, we solve for the mass and find it to be approximately 2.08 kg.

V=u+gtv=0+9.8*2v=19.6m/sKE=1/2*mv²400*2=m*19.6²800/384.16=m2.08kg=m