8. At time t=0, a ball is thrown vertically upward from the ground level, reaching its maximum height and returning back to the ground level. Which velocity versus time graph describes its motion? Take the upward direction as the positive direction. (a) (b) (d)

A ball is projected vertically upward at time t = 0.00 s, from the ground and experiences negligible air resistance. The ball rises, then falls and strikes the ground. The initial velocity of the ball is 20 m/s. The time when it is 9 m above the ground and moving downwards is (in seconds)

A particle moves along the x axis. It is initially at the position 0.330 m, moving with velocity 0.250 m/s and acceleration -0.330 m/s?. Suppose it moves with constant acceleration for 3.40 s. (a) Find the position of the particle after this time. m (b) Find its velocity at the end of this time interval. m/s We take the same particle and give it the same initial conditions as before. Instead of having a constant acceleration, it oscillates in simple harmonic motion for 3.40 s around the equilibrium position x = 0. Hint: the following problems are very sensitive to rounding, and you should keep all digits in your calculator. (c) Find the angular frequency of the oscillation. Hint: in SHM, a is proportional to x. /s (d) Find the amplitude of the oscillation. Hint: use conservation of energy. (e) Find its phase constant o, if cosine is used for the equation of motion. Hint: when taking the inverse of a trig function, there are always two angles but your calculator will tell you only one…

A model rocket is launched straight upward with an initial speed of 53.0 m/s. It accelerates with a constant upward acceleration of 1.50 m/s2 until its engines stop at an altitude of 190 m. (a) What can you say about the motion of the rocket after its engines stop? This answer has not been graded yet. (b) What is the maximum height reached by the rocket? m (c) How long after liftoff does the rocket reach its maximum height? (d) How long is the rocket in the air?

A)  Compute the position of the sandbag at a time 1.25 s after its release.      Express your answer in meters.   B)  Compute the magnitude of the velocity of the sandbag at a time 1.25 s       after its release.       Express your answer in meters per second.

A rock is thrown vertically upward from ground level at time t = 0.At t = 1.5 s it passes the top of a tall tower, and 1.0 s later it reaches its maximum height.What is the height of the tower?

A swimmer bounces straight up from a diving board and falls feet first into a pool. She starts with a velocity of 4.0 m/s, and her takeoff point is 1.1 m above the pool.  Which of these two valid methods is the easiest to find how long her feet are in the air? Group of answer choices Break the problem in two parts. For part 1, find the time to reach her highest point by using v0 = 4 m/s, a = -9.8 m/s2, and vf = 0 m/s.  For part 2, you can use the highest point above the board found in the previous problem and add it to her height above the pool. Then, using v0 = 0 m/s and a = -9.8 m/s2, you can find the time to reach the ground. Since you only care about the end points in this case, you can use v0 = 4 m/s, a = -9.8 m/s2, and Δy = -1.1 m to find the time to reach the ground.

A particle moves from an initial position with coordinates x = -2.0 m, y = +3.0 m, to a final position with coordinates x = +5.0 m, y = +7.0 m in a time interval of 10 s. What is the magnitude of the average velocity for this displacement?

17. Sketch a graph that is a possible description of position as a function of time for a particle that moves along the x axis and, at t = 1 s, has (a) zero velocity and positive acceleration; (b) zero velocity and negative acceleration; (c) negative velocity and positive acceleration; (d) negative velocity and negative acceleration. (e) For which of these situations is the speed of the particle increasing at t = 1 s?

A catapult launches a test rocket vertically upward from a well, giving the rocket an initial speed of 80.8 m/s at ground level. The engines then fire, and the rocket accelerates upward at 3.90 m/s2 until it reaches an altitude of 1200 m. At that point its engines fail, and the rocket goes into free fall, with an acceleration of −9.80 m/s2 For what time interval is the rocket in motion above the ground? What is the maximum altitude? What is its velocity just before it hits the ground?