A particle which moves in two-dimensional curvilinear motion has coordinates in millimeters which vary with time t in seconds according to x = 5t² + 7.9 and y = 5t3 + 3.3. For time t = 4.1 s, determine the radius of curvature p of the particle path and the magnitudes of the normal and tangential accelerations.

A pursue at radius 2.00 m and a wallet at radius 3.00 m travel in uniform circular motion on the floor of a merry-go-round as the ride turns. They are on the same radial line. At one instant, the acceleration of the pursue is (2.00 m/s^2)i + (4.00 m/s^2)j. At the instant and in unit-vector notation, what is the acceleration of the wallet?

A woman rides a carnival Ferris wheel at radius 22 m, completing 4.1 turns about its horizontal axis every minute. What are (a) the period of the motion, and the magnitude of her centripetal acceleration at (b) the highest point and (c) the lowest point?

A carnival merry-go-round rotates about a vertical axis at a constant rate. A man standing on the edge has a constant speed of 3.30 m/s and a centripetal acceleration of magnitude 2.01 m/s². Position vector locates him relative to the rotation axis. (a) What is the magnitude of 7? What is the direction of 7 when a is directed (b) due east and (c) due south? (a) Number (b) (c) Units

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.

An object is traveling around the rim of a circular track whose diameter is 45.3 m.  When it has rotated by 2π radians, what is its linear displacement (in centimeters)?

The earth rotates once per day about an axis passing through the north and south poles, an axis that is perpendicular to the plane of the equator. Assuming the earth is a sphere with a radius of 6.38 x 106 m, determine the speed and centripetal acceleration of a person situated (a) at the equator and (b) at a latitude of 28.0 ° north of the equator. Re (a) v = Units ac = Units (b) v = Units ac = Units

The aorta is a major artery, rising upward from the left ventricle of the heart and curving down to carry blood to the abdomen and lower half of the body. The curved artery can be approximated as a semicircular arch whose diameter is 4.3 cm. If blood flows through the aortic arch at a speed of 0.39 m/s, what is the magnitude (in m/s2) of the blood's centripetal acceleration? トーD- Blood from Blood to heart abdomen

Airplane makes a gradual 90 degrees turn while flying at a constant speed of 200 m/s. The process takes 20.0 seconds to complete. 1. for this turn, the magnitude of the radial acceleration of the plane is?

A particle is moving along a circular path with tangential acceleration function of a(t) = (0.12t + 0.3) m/s^2 and a radius of curvature of 5.5 m. At t = 3 seconds, a velocity of 0.4 m/s is attained. Find the magnitudes of velocity and acceleration at t = 8s