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's velocity is described by the function vₓ = (t² - 7t + 10) m/s, where t is in s. What is the particle's acceleration at each of the turning points?

Draw position, velocity, and acceleration graphs for the ball shown in FIGURE P2.44. See Problem 43 for more information.

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.

FIGURE P2.45 shows a set of kinematic graphs for a ball rolling on a track. All segments of the track are straight lines, but some may be tilted. Draw a picture of the track and also indicate the ball's initial condition.

A block is suspended from a spring, pulled down, and released. The block's position-versus-time graph is shown in FIGURE P2.38. Draw a reasonable velocity-versus-time graph.

A particle's velocity is given by the function $\(\mathcal{v}\)_x = (2.0 \, \(\text{m/s}\)) \(\sin\)(\(\pi\) t)$, where $t$ is in $s$. What is the particle's acceleration at that time?