A particle moves as x = Ae⁻ᵏᵗ, where A,k0. During 0 ≤ t ≤ T, its average speed is:

Question

A particle moves as x = Ae⁻ᵏᵗ, where A,k>0. During 0 ≤ t ≤ T, its average speed is:

G1 Physics · Accepted Answer

v = dx/dt = −Ak e⁻ᵏᵗ < 0. So the motion is monotonic and distance equals magnitude of displacement. Distance = A − Ae⁻ᵏᵀ = A(1−e⁻ᵏᵀ). Therefore average speed = A(1−e⁻ᵏᵀ)/T.