Randall D. Knight — Dynamics I: Motion Along a Line: Problem 78

a. Use what you’ve learned in calculus to prove that \( a_x = v_x \frac{dv_x}{dx} \) b. A spherical particle of mass \( m \) is shot horizontally with initial speed \( v_0 \) into a viscous fluid. Use Stokes’ law to find an expression for \( v_x(x) \), the horizontal velocity as a function of distance traveled. Vertical motion due to gravity can be ignored. c. A 3.0-cm-diameter, 9.0 g marble is shot horizontally into a tank of \( 40^{\circ}\text{C} \) honey at 80 cm/s. How far in cm will it travel before stopping?