The position of a particle moving along the x axis is given by x = 6.0t² - 1.0t³, where x is in meters and t in seconds. What is the position of the particle when it achieves its maximum speed in the positive x direction?

Nerve impulses in a human body travel at a speed of about 100 m/s. Suppose a person accidentally steps barefoot on a pebble. About how much time does it take the nerve impulse to travel from the foot to the brain (in s)? Assume the person is 1.60 m tall and the nerve impulse travels at uniform speed.

The position of a particle moving in the xy -plane is given by 7(t) = (3t2 – t³)î + (t*)j + (- 6t)k. What is the average acceleration of the particle over the time interval between t = 1 s and t = 2 s?

The position of a particle moving along the x axis is given by x(t) = 7t² - 1.7t³, where x is in meters and t in seconds. What is the position of the particle when it achieves its maximum speed in the positive x direction?

A particle starts from the origin at r=0 with a velocity of 8.0 m/s and moves in the xy plane with constant acceleration (3.5i +1.7)) m/s1. (a) When the particle's x coordinate is 27 m, what is its y coordinate? (b) When the particle's x coordinate is 27 r. what is its speed? m/s

The NEXT morning, you wake up in a strange room yet again, and this time you drop a ball from a height of 1.54 m above the floor. The ball hits the floor 0.392 s after your drop it. You guess that you must have been taken to an alien planet with gravity different from Earth s. What is this planet s g (that is, the magnitude of the acceleration due to gravity on this planet)?     10.0 m/s^2     15.0 m/s^2     30.0 m/s^2     20.0 m/s^2

An object moves on xy plane according to the equation 7 = 20 cos(3t) î + (1,5t + 3,5t2)j. Determine its position at t = 0. Find its average velocity and average acceleration between t = 2s and t = 5s.

A particle is moved over an XY plane with acceleration components ax = 1.0 m/s2 and ay = -2.0 m/s2. Its initial velocity has components Vix = 8.0 m/s and Viy = 13 m/s. What is the speed of the particle after 4 seconds ?

In a laboratory test of tolerance for high acceleration, a pilot is swung in a circle 11.5 m in diameter. It is found that the pilot blacks out when he is spun at 30.6 rpm (rev/min). At what acceleration (in SI units) does the pilot black out? Express this acceleration in terms of a multiple of g. If you want to decrease the acceleration by 13.0% without changing the diameter of the circle, by what percent must you change the time for the pilot to make one circle? acceleration: acceleration as a multiple of g: percent of time change: m/s² %

The NEXT morning, you wake up in a strange room yet again, and this time you drop a ball from a height of 2.15 m above the floor. The ball hits the floor 0.265 s after your drop it. You guess that you must have been taken to an alien planet with gravity different from Earth s. What is this planet s g (that is, the magnitude of the acceleration due to gravity on this planet)?     61.2 m/s^2     30.6 m/s^2     45.9 m/s^2     97.9 m/s^2