A particle moving in the xy-plane has velocity v = (2ti + (3-t^2)j) m/s, where t is in s. What is the particle's acceleration vector at t = 4s?

The coordinates of a bird flying in the xy-plane are given by x(t) = αt and y(t) = 3.0 m − βt2, where α = 2.4 m/s and β = 1.2 m/s2. (a) Sketch the path of the bird between t = 0 and t = 2.0 s.

The position of a squirrel running in a park is given by r = [(0.280 m/s)t + (0.0360 m/s2)t2]î + (0.0190 m/s3)t3ĵ. (b) At t = 5.00 s, how far is the squirrel from its initial position?

A particle's trajectory is described by x = (1/2t^2 - 2t^2)m and y = (1/2 t^2-2t)m, where t is in s. (a) What are the particle's position and speed at t = 0 s and t = 4s?

A spaceship maneuvering near Planet Zeta is located at r = ( 600î ─ 400ĵ + 200k ) X 10³ km, relative to the planet, and traveling at v = 9500î m/s. It turns on its thruster engine and accelerates with a = ( 40î ─ 20k ) m/s² for 35 min. What is the spaceship's position when the engine shuts off? Give your answer as a position vector measured in km.

You have a remot-controlled car that has been programmed to have velocity v = (3ti + 2t^2j) m/s, where t is in s. At t = 0 s, the car is at r0 = (3.0i + 2.0j) m. What are the car's (a) position vector

Scientists design a new particle accelerator in which protons (mass 1.7 X 10^-27 kg) follow a circular trajectory given by r = c cos (kt^2) î + c sin (kt^2) ĵ, where c = 5.0 m and k = 8.0 x 10^4 rad/s^2 are constants and t is the elapsed time. a. What is the radius of the circle?

CALC A 100 g bead slides along a frictionless wire with the parabolic shape y = (2m⁻¹) x^2. a. Find an expression for aᵧ, the vertical component of acceleration, in terms of x, vₓ, and aₓ.Hint: Use the basic definitions of velocity and acceleration.