JEE Advanced2018PhysicsLaws of MotionActual
A solid horizontal surface is covered with a thin layer of oil. A rectangular block of mass m = 0.4 k g is at rest on this surface. An impulse of 1.0 N s is applied to the block at time t = 0 so that it starts moving along the x-axis with a velocity v t = v 0 e - t τ , where v 0 is a constant and τ = 4 . The displacement of the block, in meter, at t = τ is __________. Take e - 1 = 0.37
Correct answer
0
Step-by-step solution
v = v 0 e - t τ v 0 = J m = 2.5 m / s v = v 0 e - t τ d x d t = v 0 e - t τ ∫ 0 x d x = v 0 ∫ 0 τ e - t τ d t ∫ e - x d x = e - x - 1 x = v 0 e - t τ - 1 τ 0 τ x = 2.5 - 4 e - 1 - e 0 x = 25 - 4 0.37 - 1 x = 6.30