The following forces are acting on a $250\mathrm{g}$ box on a horizontal surface. A downward force of gravity with magnitude $2.45\mathrm{N}$. An upward normal force with magnitude $2.45\mathrm{N}$. A rightward pull from a rope of $5.0\mathrm{N}$. A leftward kinetic friction force with magnitude $7.5\mathrm{N}$. At this instant, what is the magnitude of the acceleration of the box?

(III) Air resistance acting on a falling body can be taken into account by the approximate relation for the acceleration: a = dv/dt = g ― kv , where k is a constant. (

b) Determine an expression for the terminal velocity, which is the maximum value the velocity reaches.

(II) A 2.0-kg purse is dropped from the top of the Leaning Tower of Pisa and falls 55 m before reaching the ground with a speed of 27m/s . What was the average force of air resistance?

(II) The terminal velocity of a 3 x 10⁻⁵ kg raindrop is about 9 m/s. Assuming a drag force F_D = -bv , determine (b) the time required for such a drop, starting from rest, to reach 63% of terminal velocity.

An 800-kg car is traveling along a horizontal road directly towards a cliff. The driver notices and brakes, resulting in a 5,000-N net force slowing the car down. If the car's initial speed was 20 m/s and the car stops just before going over the cliff, how far away was the car from the cliff when the driver hit the brakes?

(II) A child on a sled reaches the bottom of a hill with a velocity of 10.0 m/s and travels 25.0 m along a horizontal straightaway to a stop. If the child and sled together have a mass of 60.0 kg, what is the average retarding force on the sled on the horizontal straightaway?