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- An object is moving along the x-axis. At t = 0 it is at x = 0. Its x-component of velocity Vx as a function of time is given by: Vx(t) = at - Bt3, where a = 6.8 m/s2 and B = 4.0 m/s4 I. At what nonzero time t is the object again at x = 0? (Express your answer with the appropriate units.) II. At t = 1.8 s, what is the x-component of the velocity of the object? (Express your answer with the appropriate units.) III. At t = 1.8 s, what is the x-component of the acceleration of the object? (Express your answer with the appropriate units.)arrow_forwardOn a spacecraft two engines fire for a time of 389 s. One gives the craft an acceleration in the x direction of ax = 3.41 m/s^2, while the other produces an acceleration in the y direction of ay = 7.34 m/s^2. At the end of the firing period, the craft has velocity components of vx = 1860 m/s and vy = 4290 m/s. Find the (a) magnitude and (b) direction of the initial velocity. Express the direction as an angle with respect to the +x axis.arrow_forwardThe velocity v→ of a particle moving in the xy plane is given by v→=(5.50t-5.00t2)î+9.00ĵ, with v→ in meters per second and t (> 0) in seconds. At t = 1.40 s and in unit-vector notation, At what positive time does the speed equal 10.0 m/s?arrow_forward
- A glider is initially moving at a constant height of 3.76 m. It is suddenly subject to a wind such that its velocity at a later time t can be described by the equation v(t) = 16.18 − 7.78(1 + t) + 0.70t3, where v and its components are in meters per second, t is in seconds, and the z axis is perpendicular to the level ground. (a) What was the initial velocity of the glider? (Express your answer in vector form.) vi = m/s(b) Write an expression for the acceleration of the glider in component form when t = 2.14 s. (Express your answer in vector form.) a(t = 2.14 s) = m/s2arrow_forwardAn animal has a coordinates of (1.1 m, 3.4 m) at time t1 = 0 and when t2= 3.0 s, it is located at (5.3 m, -0.5 m). For this time interval, find (a) the components of the average velocity, and (b) the magnitude and direction of the average velocity.arrow_forwardA particle moves in the xy plane, starting from the origin at t = 0 with an initial velocity having an x component of 20 m/s and a y component of 215 m/s. The particle experiences an acceleration in the x direction, given by ax =4.0 m/s2.(A) Determine the total velocity vector at any later time. (B) Calculate the velocity and speed of the particle at t = 5.0 s and the angle the velocity vector makes with the x axis. (C) Determine the x and y coordinates of the particle at any time t and its position vector at this time.arrow_forward
- A particle is moving on xy plane, with x=15sin(2t), and y = 20cos(2t) Find the magnitude of the velocity as a function of timearrow_forwardA rabbit runs across a parking lot on which a set of coordinate axis has been drawn. The coordinates of the rabbit’s position as a function of time t are given by: x = -0.3t2 + 5t + 28 and y = 0.22t2 - 8t + 30 with t in seconds and x and y in meters. What is the velocity at t= 10 sec? A. 0.6 i + 0.4 j B. -0.2i +1.6j +30 C. -i - 3.6 j D. 4i + 2jarrow_forwardA classic physics problem states that if a projectile is shot vertically up into the air with an initial velocity of 146 feet per second from an initial height of 89 feet off the ground, then the height of the projectile, hh, in feet, tt seconds after it's shot is given by the equation: h=−16t2+146t+89h=-16t2+146t+89 Find the two points in time when the object is 126 feet above the ground (to one decimal places). Answer: The object is 126 feet off the ground at the following times: (Enter your two answers separated by a comma. Round to ONE decimal places.)arrow_forward
- A projectile is fired in the air from a height of 125 feet. Its velocity (in feet per second) t seconds after launch is f(t), given in the following table. x 0 5 10 15 20 25 30 f(x) 230 211 196 167 155 122 108 a) How fast is the projectile traveling 15 seconds after launch? b) How far does the projectile move between 5 seconds and 25 seconds? c) How far does the projectile move between 0 seconds and 15 seconds? d) How high is the projectile at 25 seconds? It isarrow_forwardA blue car of length 4.52 m is moving north on a roadway (hat intersects another perpendicular roadway (Fig. P2.81, page 58). The width of the intersection from near edge to far edge is 28.0 m. The blue car has a constant acceleration of magnitude 2.10 m/s2 directed south. The time interval required for the nose of the blue car to move from the near (south) edge of the intersection to the north edge of the intersection is 3.10 s. (a) How far is the nose of the blue car from the south edge of the intersection when it stops? (b) For what time interval is any part of the blue car within the boundaries of the intersection? (c) A red car is at rest on the perpendicular intersecting roadway. As the nose of the blue car enters the intersection, the red car starts from rest and accelerates east at 5.60 m/s2. What is the minimum distance from the near (west) edge of the intersection at which the nose of the red car can begin its motion if it is to enter the intersection alter the blue car has entirely left the intersection? (d) II the red car begins its motion at the position given by the answer to pan (c), with what speed does it enter the intersection?arrow_forwardUnder which of the following conditions is the magnitude of the average velocity of a particle moving in one dimension smaller than the average speed over some time interval? (a) A particle moves in the +x direction without reversing. (b) A particle moves in the x direction without reversing. (c) A particle moves in the +x direction and then reverses the direction of its motion. (d) There are no conditions for which it is true.arrow_forward
- Principles of Physics: A Calculus-Based TextPhysicsISBN:9781133104261Author:Raymond A. Serway, John W. JewettPublisher:Cengage LearningGlencoe Physics: Principles and Problems, Student...PhysicsISBN:9780078807213Author:Paul W. ZitzewitzPublisher:Glencoe/McGraw-HillPhysics for Scientists and Engineers, Technology ...PhysicsISBN:9781305116399Author:Raymond A. Serway, John W. JewettPublisher:Cengage Learning