A crate slides across a frictionless horizontal surface with constant acceleration 4.15 m/s2 and over a time interval reaches a final velocity of 10.0 m/s.
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- A student at the top of a building of height h throws one ball upward with a speed of vi and then throws a second ball downward with the same initial speed vi. Just before it reaches the ground, is the final speed of the ball thrown upward (a) larger, (b) smaller, or (c) the same in magnitude, compared with the final speed of the ball thrown downward?A crate slides across a frictionless horizontal surface with constant acceleration 4.10 m/s2 and over a time interval reaches a final velocity of 12.2 m/s.If its initial velocity is 6.10 m/s, what is its displacement (in m) during the time interval? (Indicate the direction with the sign of your answer.)(B) What is the distance it travels (in m) during this interval? (C) If its initial velocity is −6.10 m/s, what is its displacement (in m) during the time interval? (Indicate the direction with the sign of your answer.) (D)What is the total distance it travels (in m) during the interval in part (c)?rocket, on an unknown planet, launches straight upward. Starting from rest, the rocket accelerates until it reaches 25 m/s then maintains that velocity until its boosters shut off. It eventually falls back to the planet. ASSUME: Starting at t = 0, the rocket accelerates upwards a total distance of 10 m, where it reaches an instantaneous velocity of 25 m/s The moment it reaches an instantaneous velocity of 25 m/s, it travels 30 m upward at a constant speed, then the engines cut off. The moment the engines cut off: the rocket is in free fall From the time it initially launches (t = 0) to the time it lands back on the planet is 7 s The acceleration due to gravity is constant on this planet. HOWEVER you may not assume g = 10 m/s2 Air resistance is negligible DETERMINE: The acceleration due to gravity on this planet
- A bolt is dropped from a bridge under construction, falling 94 m to the valley below the bridge. (a) In how much time does it pass through the last 33% of its fall?s(b) What is its speed when it begins that last 33% of its fall?m/s(c) What is its speed when it reaches the valley beneath the bridge?m/sA ball is thrown straight up from the edge of the roof of a building. A second ball is dropped from the roof a time of 1.12 s later. You may ignore air resistance. If the height of the building is 20.4 m, what must the initial speed be of the first ball if both are to hit the ground at the same time? Consider the same situation, but now let the initial speed v0 of the first ball be given and treat the height h of the building as an unknown. What must the height of the building be for both balls to reach the ground at the same time for v0 = 8.50 m/s. If v0 is greater than some value vmax, a value of h does not exist that allows both balls to hit the ground at the same time. Solve for vmax. If v0 is less than some value vmin, a value of h does not exist that allows both balls to hit the ground at the same time. Solve for vmin.The acceleration of a particle is given by ax(t) = -2.03 m/s2+ (2.93 m/s2)t I. Find the initial velocity V0x such that the particle will have the same x-coordinate at time t = 3.97 t as it had at t=0. (Express your answer in meters per second.) II. What will be the velocity of time t = 3.97 s? (Express your answer in meters per second.)
- a) The velocity of a particle changes from v1 = 2i + 5j -3k m/s to V2 = 5i- 7j+ 2k m/s in 2 s. What is its average acceleration? b) Aparticle has an acceleration of a = -7i + 3j m/s2 for a period of 4 s. After this time the velocity is V2= 6i - 2km/s. What was the initial velocity?Superman starting from rest has an acceleration of 10m/s2 up. He makes it 127m into theair before he’s exposed to kryptonite and is only under the influence of gravity.(a) How long after take off is Superman exposed to kryptonite?(b) What is Superman’s velocity when he is exposed to the kryptonite?(c) What is the maximum height Superman reaches?(d) What is the total amount of time Superman is in the air?A particle moves along the x axis. Its x coordinate varies with time according to the expression x = 3t° – 2t +5, where x is in meters and t is in seconds. a) Determine the displacement of the particle in the time intervals t=1s to t=3s. b) Calculate the average velocity in the time intervals t=1s to t=3s. c) Find the instantaneous velocity of the particle at t=2.5s. d) Calculate the average acceleration in the time intervals t=1s to t=3s. e) Find the instantaneous acceleration of the particle at t=2.5s.
- a,b,c is answered, just need d. You carefully observe an object moving along the x-axis and determine that its position as afunction of time is given by; x(t) = 2t − 3t^2+ t^3. (a) What is the position at time t = 2s? = 0m (b) What is the velocity at time t = 2s? = 2m/s (c) What is the acceleration at time t = 2s? = 6m/s^2 (d) how far did it travel between times t = 0s and t = 2s? (Distance not displacement, plot x vs. t graph)A box slides across a frictionless horizontal surface with constant acceleration 3.60 m/s and over a time interval reaches a final velocity of 13.4 m/s. (a) If its initial velocity is 6.70 m/s, what is its displacement (in m) during the time interval? (Indicate the direction with the sign of your answer.) (b) What is the distance it travels (in m) during this interval? m (c) If its initial velocity is -6.70 m/s, what is its displacement (in m) during the time interval? (Indicate the direction with the sign of your answer.) m (d) What is the total distance it travels (in m) during the interval in part (c)?The velocity of a particle is given by v = 23t2 - 110t + 52, where v is in meters per second and t is in seconds. Plot the velocity v and acceleration a versus time for the first 6.4 seconds of motion and evaluate the velocity when a is zero. Make the plots and then answer the questions. Questions: When t = 0.8 s, V = i m/s, a = i m/s2 When t = 3.7 s, V = i m/s, a = i m/s? When t = 4.7 s, V = i m/s, a = i m/s? When a = 0, V = m/s