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?

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 = (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?

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?

When a 1984 Alfa Romeo Spider sports car accelerates at the maximum possible rate, its motion during the first 20 s is extremely well modeled by the simple equation v_x² = (2P/m)t, where P = 3.6 ✕ 10⁴ watts is the car's power output, m = 1200 kg is its mass, and v_x is in m/s. That is, the square of the car's velocity increases linearly with time. Find an algebraic expression in terms of P, m, and t for the car's acceleration at time t.

A car's velocity as a function of time is given by$v_x(t) = α + βt^2$, where $α = 3.00$ m/s and $β = 0.100$ m/s³. Draw $v_x$-$t$ and $a_x$-$t$ graphs for the car's motion between $t=0$ and $t=5.00$ s.

A turtle crawls along a straight line, which we will call the $x$-axis with the positive direction to the right. The equation for the turtle's position as a function of time is $x(t) = 50.0$ cm + ($2.00$ cm/s)$$$t$ − ($0.0625$ cm/s²)$t^2$. Sketch graphs of $x$ versus $t$, $v_x$ versus $t$, and $a_x$ versus $t$, for the time interval $t=0$ to $t=40$ s.