A motorboat is moving in a straight line on a lake with an initial velocity v . When its engine is shut off, it experiences a uniform deceleration due to water resistance. After coasting for a distance of 60 m , its velocity decreases to v 2 . What is the total distance covered by the boat from the moment the engine was shut off until it comes to rest?

Step-by-step solution

Using the third equation of motion, v^2 = u^2 + 2as . For the first part of the motion, the initial velocity is v , final velocity is v 2 , and distance s = 60 m . ( v 2 )^2 = v^2 + 2a(60) v^2 4 - v^2 = 120a - 3v^2 4 = 120a a = - v^2 160 Let the total distance covered before coming to rest be S . The final velocity is 0 . 0 = v^2 + 2aS 0 = v^2 + 2 (- v^2 160 )S v^2 80 S = v^2 S = 80 m Answer: 80 m