The position of a particle moving along the x axis is given by x = (21 + 22t-6.0t2) m,where t is in s. What is the instantaneous velocity at t= 1.0 s?

A bowling ball traveling with constant speed hits the pins at the end of a bowling lane 16.5 m long. The bowler hears the sound of the ball hitting the pins 2.61 s after the ball is released from his hands. What is the speed of the ball (in m/s), assuming the speed of sound is 340m/s?

A particle's velocity is described by the function vx = t^2− 10t+7m/s, where t is in s How many turning points does the particle reach.

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?

A particle has a position in space given by r = 2t^3 i + 4t^2 j - 3t k where r is in m and t in seconds. Find the magnitude of the instantaneous velocity at t = 3.0 s. 24 m/s 75 m/s 54 m/s 59 m/s

A ball is thrown upward from the top of a 40.0 m tall building. The ball's initial speed is 12.0 m/s. At the same instant, a person is running on the ground at a distance of 23.0 m from the building. What must be the average speed of the person if he is to catch the ball at the bottom of the building?

The acceleration of a particle is a constant. At t = 0 the velocity of the particle is (15.8î + 18.4ĵ) m/s.At  = 3.6 s the velocity is 10.5ĵ m/s. (Use the following as necessary: t. Do not include units in your answers.)   (b) How do the position (in m) and velocity (in m/s) vary with time? Assume the particle is initially at the origin.

The displacement of a particle is given by s = 4t³ - 60t² + 100t -58 where s is in feet and t is in seconds. Plot the displacement, velocity, and acceleration as functions of time for the first 13 seconds of motion. After you have made the plots, answer the questions. Questions: At t = 1.8 S= i fty = i ft/seca = i ft/ser sec, At t = 6.6 i S= fty = i ft/seca = i ft/se sec, Att = 9.8 sec, i fty = ft/seca = S = i ft/ser The velocity is zero when t = i sec and when t = sec