A particle moves according to a law of motion s = f(t), t ≥ 0, where t is measured in seconds and s in feet. (If an answer does not exist, enter DNE.)  f(t) = t3 − 9t2 + 24t a) When is the particle moving in the positive direction? (Enter your answer using interval notation.) b) Find the acceleration (in ft/s2) at time t and after 1 second. c) Answer using interval notation- when is the particle speeding up and slowing down?

An object's position as a function of time in one dimension is given by the expression; 3.89t2 + 2.22t + 7.48 where are constants have proper SI Units. What is the object's average velocity between the times t = 3.16 s and t = 8.38 s? with everything in 3 sig figs

Pls help ASAP

A woman stands at the edge of a cliff and throws a rock horizontally over the edge with a speed of v, = 19.5 m/s. The rock leaves her hand at a height of h = 49.0 m above level ground at the bottom of the cliff, as shown in the figure. Note the coordinate system in the figure, where the origin is at the bottom of the cliff, directly below where the rock leaves the hand. (a) What are the coordinates of the initial position of the rock? (Enter your answers in m.) m Yo = (b) What are the components of the initial velocity? (Enter your answers in m/s.) Vox = m/s Voy m/s

Please Asap

roportionality constant b = 50 N-sec/m, determine the equation of motion of the object. When will the object strike the ground? [Hint: Here the exponentia pproximate the time t when the object strikes the ground.] Assume that the acceleration due to gravity is 9.81 m/sec". et x(t) represent the distance the object has fallen in t seconds. Determine the equation of motion of the object.

An unidentified flying object (UFO) is observed to travel a total distance of 49000 m, starting and ending at rest, over a duration of 3.07 s. Assuming the UFO accelerated at a constant rate to the midpoint of its journey and then decelerated at a constant rate the rest of the way, what was the magnitude of its acceleration? Express your answer in g s , where 1 g = 9.81 m/s^2.     20,796 g s     10,398 g s     2,120 g s     1,060 g s

A person stands at the edge of a cliff and throws a rock horizontally over the edge with a speed of v = 23.0 m/s. The rock leaves his hand at a height of h = 43.0 m above level ground at the bottom of the cliff, as shown in the figure. Note the coordinate system in the figure, where the origin is at the bottom of the cliff, directly below where the rock leaves the hand. 4 7 i (a) What are the coordinates of the initial position of the rock? (Enter your answers in m.) Xo = Yo = m (b) What are the components of the initial velocity? (Enter your answers in m/s.) Vox = m/s m/s Voy

One of the fastest known animals is the Indian spine-tailed swift. A swift flies 2.80 km due north in a time of 32.8 s. a. What is its average velocity due north in meters per second? Enter a positive value if the average velocity is due north and enter a negative value if it is due south. answer in m/s b. What is its average velocity due north in miles per hour? Enter a positive value if the average velocity is due north and enter a negative value if it is due south. anser in mi/h

Mr. M gets on his bike and rides 11m in the direction of [E52S]. He then changes his direction to [W11N] and rides another 5.7m. a) What was his total displacement? b) What was his distance traveled?