A 4 kg object is pushed with a force of 20 N over a distance of 3 m. If the object starts from rest, what is its final speed? (Assume no friction)

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Q: A 4 kg object is pushed with a force of 20 N over a distance of 3 m. If the object starts from rest, what is its final speed? (Assume no friction)

Solution: Work done = Force × Distance = 20 N × 3 m = 60 J. Kinetic energy = 0.5 × m × v². 60 J = 0.5 × 4 kg × v². v² = 30, v = √30 ≈ 5.48 m/s.

Steps: 9

Step 1: Identify the given values. The mass of the object (m) is 4 kg, the force applied (F) is 20 N, and the distance moved (d) is 3 m.
Step 2: Calculate the work done on the object using the formula: Work done = Force × Distance. So, Work done = 20 N × 3 m.
Step 3: Perform the multiplication: 20 N × 3 m = 60 J. This means 60 Joules of work is done on the object.
Step 4: Understand that the work done on the object is converted into kinetic energy. The formula for kinetic energy (KE) is KE = 0.5 × m × v², where v is the final speed.
Step 5: Set the work done equal to the kinetic energy: 60 J = 0.5 × 4 kg × v².
Step 6: Simplify the equation: 60 J = 2 kg × v² (since 0.5 × 4 kg = 2 kg).
Step 7: Divide both sides by 2 kg to isolate v²: v² = 60 J / 2 kg = 30.
Step 8: Take the square root of both sides to find v: v = √30.
Step 9: Calculate the square root of 30, which is approximately 5.48 m/s.