The position of an object is given by vector r = (-4.00t cap i + 6.00t^3 cap j)

Question

The position of an object is given by vector r = (-4.00t cap i + 6.00t^3 cap j) m where i is in seconds. At t = 2.0 s, what is the magnitude of the particle's acceleration? 0 m/s^2 2.0 m/s^2 17 m/s^2 36 m/s^2 72 m/s^2 Two identical balls are at rest and side by side at the top of a hill. You let one ball, A, start rolling down the hill. A later you start the second ball B, down the hill by giving it a shove. The second ball rolls down the hill along a line parallel to the path of the first ball and passes it. At the instant hall B passes ball A: it has the same position and the same velocity as A. it has the same position and the same acceleration as A. it has the same velocity and the same acceleration as A. it has the same displacement and the same velocity as A. it has the same position, displacement and velocity as A. A carnival Ferris w heel has a 15-m radius and completes five turns about its horizontal axis every minute. What is acceleration of a passenger at his lowest point during the ride? 5.7 m/s^2 downward 4.1 m/s^2 upward 14 m/s^2 downward 4.1 m/s^2 downward 19 m/s^2 downward The vector r vector indicates the instantaneous displacement of a projectile from the origin. At the instant when the projectile is at vector r. its velocity and acceleration vectors are vector v and vector a Which statement is correct? vector v is always perpendicular to vector r. vector a is always perpendicular to vector r. vector a is always perpendicular to vector v. vector a is always perpendicular to vector v_x. vector a is always perpendicular to vector v_y.

Explanation / Answer

Position vector r = -4t i +6t 3 j

Velocity v = dr / dt

= -4 i + 6(3t 2 ) j

= -4 i + 18t 2 j

Accleration a = dv / dt

= 18(2t) j

= 36 t j

Time t= 2 s

So, a = 36(2) j

= 72 m/s 2 j

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