Two objects of mass 5 kg and 8 kg are at rest. F₁ and F₂ are the forces applied on both the boxes respectively. If the speed of both the objects after 5 seconds become 16m/sec and 15 m/sec respectively, then find the value of  F₁+F₂

From Newton’s second law, for constant force: F = m a.
Since each object starts from rest and reaches speed v in time t, the (constant) acceleration is a = (v - 0) / t = v / t.

Given

• Object 1: mass m₁ = 5 kg, final speed v₁ = 16 m/s
• Object 2: mass m₂ = 8 kg, final speed v₂ = 15 m/s
• Time for both: t = 5 s

Step 1: Accelerations

Object 1: a₁ = v₁ / t = 16 / 5 = 3.2 m/s²
Object 2: a₂ = v₂ / t = 15 / 5 = 3 m/s²

Step 2: Forces

Object 1: F₁ = m₁ a₁ = 5 × 3.2 = 16 N
Object 2: F₂ = m₂ a₂ = 8 × 3 = 24 N

Step 3: Sum of the Forces

F₁ + F₂ = 16 N + 24 N = 40 N

Answer

F₁ + F₂ = 40 N.