An object with cross section A is shot horizontally across frictionless ice. Its initial velocity is v_0x at t₀ = 0 s. Air resistance is not negligible.

a. Show that the velocity at time t is given by the expression

b. A 1.6-m-wide, 1.4-m-high, 1500 kg car with a drag coefficient of 0.35 hits a very slick patch of ice while going 20 m/s. If friction is neglected, how long will it take until the car’s speed drops to 10 m/s? To 5 m/s?

c. Assess whether or not it is reasonable to neglect kinetic friction.