A spherical ball is dropped from rest into a long column of a highly viscous liquid. Which of the following descriptions best represents the variation of the magnitude of the ball's acceleration ( a ) as a function of time ( t )?

Step-by-step solution

When the ball is dropped from rest, its initial velocity is zero. The viscous drag force is initially zero. The initial acceleration is at its maximum, determined by the effective weight (gravity minus buoyancy). As the ball falls and gains velocity, the upward viscous drag force ( F_v = 6 r v ) increases. The net downward force decreases, which means the acceleration decreases. According to Newton's second law, ma = W_ eff - F_v . Thus, a = a₀ - 6 r m v . Since velocity increases and approaches a constant terminal