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?

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?

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

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.

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)t2. (e) Sketch graphs of x versus t, υx versus t, and ax versus t, for the time interval t = 0 to t = 40 s.

A rubber ball bounces. We'd like to understand how the ball bounces.a. A rubber ball has been dropped and is bouncing off the floor. Draw a motion diagram of the ball during the brief time interval that it is in contact with the floor. Show 4 or 5 frames as the ball compresses, then another 4 or 5 frames as it expands. What is the direction of a during each of these parts of the motion?