A boat of mass 700 ~kg is travelling at a speed of 24 ~ms ⁻¹ when its engine is shut off. The magnitude of frictional force f between boat and water is given as f=35 v . Where v is the speed in ms ⁻¹ and f is in newton. The speed of boat becomes 6 ~ms ⁻¹ in time.

Step-by-step solution

Given, Mass of boat, m=700 ~kg Initial speed of boat, v₁=24 ~ms ⁻¹ Final speed of boat, v₂=6 ~ms ⁻¹ Frictional force, f=35 v According to Newton's second law, f=-m d v d t aligned 35 v & =-m d v d t d v v & = -35 m d t _ v₁ ^ v₁ d v v & = -35 m ₀^t d t ( v₂ v₁ ) & = -35 t m t & = -m 35 ( v₂ v₁ )= -700 35 ( 6 24 ) & =-20 1 4 =-20( 1- 4) & =-20 (0- 2^2 ) & =-20(-2 2) & =40 2 & =27.73 & 28 ~s aligned