f acceleration is a function of displacement, integrate a ds = v dv to obtain the velocity as a function of position. TRUE OR FALSE indeed asap thank you:>

A daring ranch hand sitting on a tree limb wishes to drop vertically onto a horse galloping under the tree. The constant speed of the horse is 10.0 m/s, and the distance from the limb to the level of the saddle is 3.00 m. (a) What must be the horizontal distance between the saddle and limb when the ranch hand makes his move? (b) For what time interval is he in the air?

The position of a particle moving along the x -axis varies with time according to x(t)=5.0t24.0t3 . Find (a) the velocity and acceleration of the particle as functions of time, (b) the velocity and acceleration at t=2.0s , (c) the time at which the position is a maximum, (d) the time at which the velocity Is zero, and (e) the maximum position.

Calculate the displacement and velocity at times of (a) 0.500, (b) 1.00, (c) 1.50, (d) 2.00, and (e) 2.50 s for a rock thrown straight down with an initial velocity of 14.0 m/s from the Verrazano Narrows Bridge in New York City. The roadway of this bridge is 70.0 m above the water.

A speedboat increases its speed uniformly from vi = 20.0 m/s to Vf = 30.0 m/s in a distance of 2.00 102 m. (a) Draw a coordinate system for this situation and label the relevant quantities, including vectors, (b) For the given information, what single equation is most appropriate for finding the acceleration? (c) Solve the equation selected in part (b) symbolically for the boats acceleration in terms of vf, vi, and x. (d) Substitute given values, obtaining that acceleration, (e) Find the time it takes the boat to travel the given distance.

A skier leaves the end of a horizontal ski jump at 22.0 m/s and falls through a vertical distance of 3.20 m before landing. Neglecting air resistance, (a) how long does it take the skier to reach the ground? (b) How far horizontally docs the skier travel in the air before landing? (Sec Section 3.4.)

In the particle under constant acceleration model, we identify the variables and parameters vxi, vxf, ax, t, and xf xi. Of the equations in Table 2.2, the first does not involve xf xi, the second does not contain ax, the third omits vxf, and the last leaves out t. So, to complete the set, there should be an equation not involving vxi. (a) Derive it from the others. (b) Use the equation in part (a) to solve Problem 23 in one step.

A particle travels in a circle of radius 10 m at a constant speed of 20 m/s. What is the magnitude of the acceleration?

Consider the following combinations of signs and values for the velocity and acceleration of a particle with respect to a one-dimensional x-axis: Velocity Acceleration a. Positive Positive b. Positive Negative c. Positive Zero d. Negative Positive e. Negative Negative f. Negative Zero g. Zero Positive h. Zero Negative Describe what the particle is doing in each case and give a real-life example for an automobile on an east-west one-dimensional axis, with east considered the positive direction.

A Lockheed Martin F-35 II lighting jet takes off from an aircraft carrier with a runway length of 90 m and a takeoff speed 70 m/s at the end of the runway. Jets are catapulted into airspace from the deck of an aircraft carrier with two sources of propulsion: the jet propulsion and the catapult. At the point of leaving the deck of the aircraft carrier, the F-35’s acceleration decreases to a constant acceleration of 5.0m/s2 at 30 with respect to the horizontal. (a) What is the initial acceleration of the F-35 on the deck of the aircraft carrier to make it airborne? (b) Write the position and velocity of the F-35 in unit vector notation from the point it leaves the deck of the aircraft carrier. (c) At what altitude is the fighter 5.0 s after it leaves the deck of the aircraft carrier? (d) What is its velocity and speed at this time? (e) How far has it traveled horizontally?