The motion of a particle is given by x = A sin3(ωt). Enter an expression for the particle's velocity, v.  Enter an expression for the particle's acceleration, a.

As illustrated in the figure, a particle P moves on an x- y plane. In this motion, x( t) = 3 2 in meters and a(y) = 4 m /s?. It is also known that the position and velocity component along the y axis both vanish. Determine the speed as well as the x and y position of the particle at i = 3s. In your opinion, is the figure correct? If not, explain why and sketch a correction. Trajectory 60 a 50 40 30 P 20 10 50 100 150 200 250

A truck travels around a circular track. The position of the truck is described by the equations (400 · cos 0) m and 0 = (0.002 · t) rad, where t is in seconds. r = r = f@) Using cylindrical coordinates, a. Determine the truck's radial and transverse components of velocity at t = 4 s, v, and vo. b. Determine the truck's radial and transverse components of acceleration at t = 4 s, a, and ag.

If we apply the above equations to the case of an object that does not change its direction of travel as it moves with constant acceleration, we find that the object: Undergoes a displacement Ax = x- x, . Note that displacement is a positive quantity if x > x, and a negative quantity if x < x,. Has average velocity v = (x - x )/t = (v + vo)/2. Note that velocity has the same sign as displacement. Travels distance d = |Ax| = |x – x,| . Note that distance is always a positive quantity. Has average speed d/t . Note that speed is always a positive quantity. Has constant acceleration a = (v – vo)/t . Acceleration may be positive or negative, depending on how velocity changes. - Xo For the case of an object that does change its direction of travel as it moves with constant acceleration, which of the quantities listed above are different? Question

A particle moves so that its position (in meters) as a function of time (in seconds) is r = î + 2t² j+ 2tk. (Use the following as necessary: t.) (a) Write an expression for its velocity as a function of time. v(t) = m/s (b) Write an expression for its acceleration as a function of time. d(t) = m/s2 Submit Answer

A particle moves according to a law of motion s = 2t^3 − 9t^2 + 12t + 1.a. Determine the velocity of the particle when it has acceleration of 2 m/s^2.b. When is the particle moving in a positive direction?

Problem 2: Kinematics and vectors. An object is moving on the xy plane with velocities given by: V₂ x = (10.0-0.500t)1 and v = (-5.00t+0.025²) j Determine the following quantities: a. The displacement of the object as a function of time. b. The average velocity of the object from for the time interval from 0 to 10 s.

This is the vx-tgraph for an object moving along the x-axis. Which of the following descriptions of the motion is most accurate? Vx The object is speeding up at an increasing rate. The object's speed is changing at a steady rate. O The object is slowing down at an increasing rate. The object is slowing down at a decreasing rate. The object is speeding up at a decreasing rate.

NASA has fired a rocket straight up into the air from ground level with an unknown initial velocity. It reaches a maximum height of 164,000 feet. This happened in Cape Canaveral therefore the rocket is under the acceleration of Earth's gavity in which we all know is -32 ft/sec/sec.                                           Please round your answers to two decimal places. a). Find the time it takes for the rocket to reach maximum height. b). find the initial velocity necessary to reach that height.