A good model for the acceleration of a car trying to reach top speed in the least amount of time is a𝓍 = a₀ ─ kv𝓍, where a₀ is the initial acceleration and k is a constant.a. Find an expression for k in terms of a₀ and the car's top speed vₘₐₓ.

Problems 49, 50, 51, and 52 show a partial motion diagram. For each:a. Complete the motion diagram by adding acceleration vectors.

Problems 49, 50, 51, and 52 show a partial motion diagram. For each:c. Draw a pictorial representation for your problem.

A steel ball rolls across a 30-cm-wide felt pad, starting from one edge. The ball's speed has dropped to half after traveling 20 cm. Will the ball stop on the felt pad or roll off?

The vertical position of a particle is given by the function y = (t^2 - 4t + 2) m, where t is in s. (b) What is the particle's position at that time?

A particle moving along the x-axis has its position described by the function x = (2t^3 + 2t + 1) m, where t is in s. At t = 2s what are the particle's (a) position

A particle's velocity is described by the function vₓ =kt² m/s, where k is a constant and t is in s. The particle's position at t₀ = 0 s is x₀ = ─9.0 m. At t₁ = 3.0 s, the particle is at x₁ = 9.0 m. Determine the value of the constant k. Be sure to include the proper units.

The position of a particle is given by the function x = (2t^3 = 6t^2 + 12) m, where t is in s. (a) At what time does the particle reach its minimum velocity? What is (vx)min?

A particle's velocity is given by the function 𝓋ₓ = (2.0 m/s) sin (πt), where t is in s.a. What is the first time after t = 0 s when the particle reaches a turning point?