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?

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.

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 moving along the x-axis has its veocity described by the function vx = 2t^2 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 (a) position

The position of a particle is given by the function x = (2t^3 = 6t^2 + 12) m, where t is in s. (b) 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 equationwhere P = 3.6 ✕ 10⁴ watts is the car's power output, m = 1200 kg is its mass, and v𝓍 is in m/s. That is, the square of the car's velocity increases linearly with time.a. Find an algebraic expression in terms of P, m, and t for the car's acceleration at time t.

CALC. 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/s^3. (c) Draw v_x-t and a_x-t graphs for the car's motion between t = 0 and t = 5.00 s.