A 3 kg object is moving with a speed of 4 m/s. If a net work of 24 J is done on

A 3 kg object is moving with a speed of 4 m/s. If a net work of 24 J is done on the object, what will be its final speed?

A 3 kg object is moving with a speed of 4 m/s. If a net work of 24 J is done on the object, what will be its final speed?

Step 1: Identify the mass of the object, which is 3 kg.
Step 2: Identify the initial speed of the object, which is 4 m/s.
Step 3: Calculate the initial kinetic energy using the formula: KE_initial = 0.5 × m × v^2.
Step 4: Substitute the values into the formula: KE_initial = 0.5 × 3 kg × (4 m/s)^2.
Step 5: Calculate (4 m/s)^2, which is 16 m^2/s^2.
Step 6: Multiply 0.5 × 3 kg × 16 m^2/s^2 to get KE_initial = 24 J.
Step 7: Identify the net work done on the object, which is 24 J.
Step 8: Calculate the final kinetic energy using the formula: KE_final = KE_initial + Work done.
Step 9: Substitute the values: KE_final = 24 J + 24 J.
Step 10: Calculate KE_final to get 48 J.
Step 11: Use the formula for final speed: v_final = √(2 × KE_final / m).
Step 12: Substitute the values: v_final = √(2 × 48 J / 3 kg).
Step 13: Calculate 2 × 48 J = 96 J.
Step 14: Divide 96 J by 3 kg to get 32 J/kg.
Step 15: Take the square root of 32 J/kg to find v_final.
Step 16: Calculate √32, which is approximately 5.66 m/s.

Kinetic Energy – The energy an object possesses due to its motion, calculated using the formula KE = 0.5 × m × v^2.
Work-Energy Principle – The principle stating that the work done on an object is equal to the change in its kinetic energy.
Final Speed Calculation – Determining the final speed of an object after work is done on it, using the relationship between kinetic energy and speed.