A block of mass 4 kg slides down an inclined surface having an inclination of 30^ with the horizontal. Starting from rest, it covers 8 m during the first two seconds. Suppose the block is pushed down the incline by a force of 4 N . Determine how far the block will move in the first two seconds after starting from rest.

Step-by-step solution

Let the initial acceleration of the block be a₁ . Using the equation of motion s = ut + 1 2 a₁ t^2 : 8 = 0 + 1 2 a₁ (2)^2 a₁ = 4 m/s ^2 The net force acting on the block initially is: F_ net = ma₁ = 4 4 = 16 N When an additional force of 4 N is applied to push the block down the incline, the new net force becomes: F'_ net = F_ net + 4 = 16 + 4 = 20 N The new acceleration of the block is: a₂ = F'_ net m = 20 4 = 5 m/s ^2 The distance covered by the block in the first two seconds with this new acceleration is: s' = u