A block of mass 2 kg, moving with the initial speed of 3 m/s comes to rest on a rough horizontal surface after travelling a distance of 3 m. The magnitude of the frictional force is :

The magnitude of the frictional force can be determined using the Work-Energy Theorem or the Equations of Motion. Both methods yield the same result.

• Given Data: Mass (m) = 2 kg, Initial velocity (u) = 3 m/s, Final velocity (v) = 0 m/s (rest), and Distance (s) = 3 m.
• Method 1: Work-Energy Theorem
  The work done by friction is equal to the change in kinetic energy (K.E.).
  Work (W) = ΔK.E.
  Frictional Force (f) × Distance (s) = ½ m(u² - v²)
  f × 3 = ½ × 2 × (3² - 0²)
  3f = 9
  f = 3 N
• Method 2: Equations of Motion
  Using v² = u² + 2as:
  0 = 3² + 2 × a × 3
  0 = 9 + 6a
  a = -1.5 m/s² (retardation)
  Force (F) = mass × acceleration = 2 kg × 1.5 m/s² = 3 N.

Therefore, the magnitude of the frictional force is 3 N, which corresponds to Option B.