Certain force acting on a 20 kg mass changes its velocity from 5 m s^–1 to 2 m s^–1. Calculate the work done by the force.

Given:
– Mass (m) = 20 kg
– Initial velocity (v_initial) = 5 m/s
– Final velocity (v_final) = 2 m/s

1. Work-Energy Principle:
– The work done (W) on an object is equal to the change in its kinetic energy (Δ KE).

2. Change in Kinetic Energy:
– The change in kinetic energy (Δ KE) formula is:
Δ KE = 1/2 x m x ( v²_final – v²_initial)

3. Calculation:
– Substituting the given values into the formula:
Δ KE = 1/2 x 20 kg x (2 m/s)² – (5 m/s)²
Δ KE = -210J

4. Result and Interpretation:
– The change in kinetic energy is -210 J
– Since work done is equal to the change in kinetic energy, the work done by the force is also -210 J
– The negative sign indicates that the work done by the force results in a decrease in the object’s kinetic energy.

Understanding these steps illustrates how the work done by a force can be calculated using the change in kinetic energy, providing insight into the change in energy associated with the object’s changing velocities due to the force applied.