A particle is moving along a circular path of 2-m radius such that its position as a function of time is given by theta = (5t^2) rad, where t is in seconds. Determine the magnitude of the particle’s acceleration when theta = 30°. The particle starts from rest when u = 0°.

The position of a particle is described byr = (t3+ 4t –4) m and θ = (t3/2) rad, where t is inseconds. Determine the magnitudes of the particle’svelocity and acceleration at the instant t = 2 s.

A marble slides down on a curved path defined by the parabola y = 0.4x2. When it is at point “A” (xA = 2m; yA = 1.6m), the velocity of the marble v = 8m/s and the tangental acceleration due to gravity is dv / dt = 4ms2. Calculate the normal component and the total magnitude of the accelarion of the mable in that instant.

A soldier is tasked with measuring the muzzle velocity of a new rifle. Knowing the principles of projectile motion, he decides to perform a simple experiment at the indoor firing range. The soldier hangs a target a distance of ?=114 m from the end of the barrel. The rifle is mounted so that the bullet exits moving horizontally at the same height as the bullseye. After six trials, the soldier tabulates the values he measured for the vertical distance ℎ from the bullseye to the bullet strike. What is the most accurate muzzle velocity that the soldier can report to his sergeant?   vm=______m/s

A particle confined to the xy-plane is in uniform circular motion around the origin. The x- and y-coordinates of the particle vary with time as follows: x(t) = r sin(cot) y(t) = r cos(cot). where >= 2.60 m and c = 2.15 s-¹. What are the x- and y-components of the particle's acceleration at an instant when x = 1.00 m and y = 2.40 m. Give your answers by entering numbers into the empty boxes below. ax || || X x² ms ms-2.

The figure below shows an object initially at point A traveling in the +x-direction. It turns in a circular path at constant speed until it is traveling in the +y-direction at point C. The quarter-circle arc from A to C is 239 m in length, and the particle moves from A to C in 33.0 s. Point B on the path is 35.0° below the x-axis. O 35.0⁰ magnitude direction C B x (a) What is the speed of the object (in m/s)? m/s (b) What is the magnitude and direction of the acceleration when the object is at point B? (Enter the magnitude in m/s² and the direction in degrees counterclockwise from the +x-axis.) m/s² ° counterclockwise from the +x-axis

A particle moves in a circular path at constant speed. The initial location of the particle is (4.24 m, 6.05 m) at t = 4 s. The velocity of the particle at this time is 3.02 m/s 3 (i.e., directed along the positive y-axis). Acceleration at this time is along the +x axis. At t=10.6 s, v is -3.02 m/s i and the acceleration is directed along the +y axis. Find the radius of the circle. For this problem assume the time interval is less than one full period. T Find the x-coordinate of the center of the circle (in meters): Xcenter m = m Question Help: Read

A particle moves in a circular path at constant speed. The initial location of the particle is (5.28 m, 6.11 m) at t = 3.6 s. The velocity of the particle at this time is 3.05 m/s 3 (i.e., directed along the positive y-axis). Acceleration at this time is along the +x axis. At t=10.76 s, vis -3.05 m/s and the acceleration is directed along the +y axis. Find the radius of the circle. For this problem assume the time interval is less than one full period. T = m Find the x-coordinate of the center of the circle (in meters): center m Question Help: Read Submit Question

a lump of wet putty moves in uniform circular motion as it rides at a radius of 20.0 cm on the rim of a wheel rotating counterclockwise with a period of 5.00 ms.The lump then happens to fly off the rim at the 5 o’clock position (as if on a clock face). It leaves the rim at a height of h = 1.20 m from the floor and at a distance d = 2.50 m from a wall.At what height on the wall does the lump hit?