A 0.2 kg rock is dropped into a lake from a few meters above the surface of the water. The rock reaches terminal velocity in the lake after 5 s in the water. During the final 3 s of its descent to the lake bottom, the rock moves at a constant speed of 4 m/s. Which of the following can be determined from the information given? a. The distance the rock travels in the first 5 s of its descent in the water b. The acceleration of the rock 2 s before it reaches the lake bottom c. The change in potential energy of the rock-Earth-water system during the final 3 s of the rock's descent. d. The speed of the rock as it enters the lake

During which of the following time intervals is the object moving in the negative direction? A. 0-4 seconds B. 4 to 7 seconds C. 7 to 10 seconds  D. All of the intervals listed above E. None of the intervals listed

An airplane needs to gain an acceleration of 0.79  m/s2  to take off on a  2000 m runway, what is the velocity ( i.e. final velocity) of the airplane just before it takes off? [Pay attention to the units in answer choices] A. 112 km/h B. 203 km/h C. 786 km/h D. 304 km/h   Please explain step by step and the equations used, thank you.

A ball is thrown upward from the ground with initial velocity vi = 19 m/s and reaches height of h above the ground before falling back down. Take the upward direction to be positive. Refer to the figure. Neglect air resistance. 1) Enter an expression for the height of the ball at a given time, h, the ball reaches in terms of the velocity at the current height vh, the initial velocity vi, and the acceleration a.  2) Enter an expression for the time it takes for the ball to travel from the ground to the a given height, Δt, in terms of the initial velocity vi, the velocity at that height vh, and the acceleration a.

Assume the three blocks portrayed in Figure P4.59 move on a frictionless surface and a 42-N force acts as shown on the 3.0-kg block. Determine (a) the acceleration given this system, (b) the tension in the cord connecting the 3.0-kg and the 1.0-kg blocks, and (c) the force exerted by the 1.0-kg block on the 2.0-kg block. 42 N 3.0 kg 1.0 kg 2.0 kg Figure P4.59

1. A ball is thrown vertically upward from the ground with a speed of 36.0 m/s. Suppose the acceleration of gravity were only 2.00 m/s² instead of 9.80 m/s² a) At what time after being thrown does the ball have a velocity of 12.0 m/s upward? b) At what time does it have a velocity of 12.0 m/s downward? c) When is the velocity of the ball zero? d) When is the displacement of the ball zero? e) What are the magnitude and direction of the acceleration while the ball is moving upward? f) What are the magnitude and direction of the acceleration while the ball is moving downward? g) What are the magnitude and direction of the acceleration when it is at the highest point?

Use the position function ?(?) = −4.9t2 + v0 + s0 for free-falling objects.  A rock is dropped from the edge of a cliff that is 176.4 meters above the water A. Determine the position function for the rock B. Find the velocity function for the rock. C. Find the velocity when t = 2 seconds. D. Find the time required for the rock to reach the surface of the water E. Find the velocity of the rock at impact with the water.

a car travels on a straight, level road. a) Starting from rest, the car is going 42 ft/s (29 mi/h) at the end of 4.5 s. What is the car's average acceleration in ft/s2? b) In 3.5 more seconds, the car is going 84 ft/s (57 mi/h). What is the car's average acceleration for this time period? (c) The car then slows to 63 ft/s (43 mi/h) in 2.5 s. What is the average acceleration for this time period? (d) What is the overall average acceleration for the total time?

A ball is thrown straight upward from a height of 3.2 m with a velocity of 13.0 m/s. a. What is the maximum height the ball reaches? b. How long does it take the ball to reach the maximum height? c. What is the total time the ball is in the air? d. With what velocity does the ball impact the surface?

The leaning tower of Pisa is 56 m tall. Supposedly Galileo investigated the behavior of falling objects by dropping them from the top of this tower and timing their descent. How long would it take an object to fall 56 m if air effects are negligible?   a. 3.33 s b. 3.38 s c. 3.83 s d. 3.88 s