A force of 6N acts horizontally on a stationary mass of 2kg for 4s. The kinetic energy gained by the mass is _________

Analyze the question: A constant force acts on a mass that starts at rest. We need the kinetic energy it gains after 4 s.

Concept: Force gives acceleration (F = ma), acceleration gives speed (v = u + at), and speed gives kinetic energy (KE = ½mv²). Equivalently, the impulse-momentum relation Ft = mv can be used.

Solution:

1. Acceleration: a = F/m = 6 / 2 = 3 m/s²

2. Final velocity (starting from rest, u = 0): v = u + at = 0 + (3)(4) = 12 m/s

3. Kinetic energy gained: KE = ½mv² = ½ × 2 × 12² = 1 × 144 = 144 J

Check using work-energy: Distance s = ½at² = ½ × 3 × 16 = 24 m Work done = F × s = 6 × 24 = 144 J ✓

Answer: C (144 J)

Tip: When a force acts on a body starting from rest for time t, a quick shortcut is KE = (Ft)² / (2m). Here: (6 × 4)² / (2 × 2) = 576 / 4 = 144 J. This skips the intermediate steps and saves time in the exam.