A particle moves according to x=Ae⁻ᵏᵗ. Its average acceleration from t=0 to t=T is:
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A particle moves according to x=Ae⁻ᵏᵗ. Its average acceleration from t=0 to t=T is:

G1 Physics · Accepted Answer

Velocity: v = dx/dt = −kAe⁻ᵏᵗ. Therefore average acceleration = [v(T)−v(0)]/T = [−kAe⁻ᵏᵀ + kA]/T = kA(1−e⁻ᵏᵀ)/T.