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.

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 = (t² - 4t + 2) m, where t is in s. What is the particle's position at that time?

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

A particle moving along the x-axis has its position described by the function x = (2t³ + 2t + 1) m, where t is in s. At t = 2s, what are the particle's position?

The position of a particle is given by the function x = (2t³ = 6t² + 12) m, where t is in s. At what time does the particle reach its minimum velocity? What is (v_x)_min?

A particle's velocity is given by the function $v_x=\left(2.0\text{m/s}\right)\sin \left(\pi t\right)$, where $t$ is in $s$. What is the first time after $t=0\text{ s}$ when the particle reaches a turning point?

A particle moving along the x-axis has its veocity described by the function v_x = 2t² m/s, where t is in s. itsinitial position is x₀ = 1 m at t₀ = 0 s. At t = 1 s, what are the particle's position?

The position of a particle is given by the function x = (2t³ - 6t² + 12) m, where t is in s. At what time is the acceleration zero?