Eduprobe
Question:
A solid horizontal surface is covered with a thin layer of oil. A rectangular block of mass m=0.4kg is at rest on this surface. An impulse of 1.0N s is applied to the block at time t=0 so that it starts moving along the x-axis with a velocity v(t)=v₀e⁻ᵗ⁄τ, where v₀ is a constant and τ=4s. The displacement of the block, in metres, at t=τ is ___________.[Take e⁻¹=0.37]Round off your answer to nearest integer.
Solution:
v = v₀e⁻ᵗ⁄τ
v₀ = J/m = 2.5 m/s
v = v₀e⁻ᵗ⁄τ
dx/dt = v₀e⁻ᵗ⁄τ
∫₀ˣ dx = v₀∫₀ᵗ e⁻ᵗ⁄τ dt
∫e⁻ˣ dx = e⁻ˣ(-1)
x = v₀[e⁻ᵗ⁄τ(-τ)]₀ᵗ
x = v₀τ(1 - e⁻ᵗ⁄τ)
For t = τ
x = 2.5(4)(1 - e⁻¹)
x = 10(1 - 0.37)
x = 10(0.63)
x = 6.30 ≈ 6