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Chapter 1 Solutions
Classical Dynamics of Particles and Systems
- A space shuttle’s coordinates as functions of time are given by x(t) = 7.0 t^3 and y(t) = 4.0t^2 - 2.1t , where x and y are in meters and t is in seconds. write a vector expression for the ball's position as a function of time.arrow_forwardA particle starts from the origin of a three-dimensional coordinate system and undergoes two consecutive displacements: r 1 → = 2.0 m i ^ + 1.0 m j ^ + 3.0 m k ^ r 2 → = − 1.0 m i ^ − 3.0 m j ^ − 1.0 m k ^ What is the distance of the particle from the origin after these two displacements?arrow_forwardIf two vectors A and B have the values A = 2i + 3j – 4k and B = 3i – 4j + 2k, find the result of A x B; A x (A x B); B x (A x B).arrow_forward
- The 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_forwardAt t = 0 the coordinates of a particle are x = 0, y = 1.98 m. At a time 0.95 s later, its coordinates are x = 3.21 m, y = 4.20 m. Find the components of the particle's average velocity during this time interval. vx = vy =arrow_forwardYou are exploring a planet and drop a small rock from the edge of a cliff. In coordinates where the +y direction is downward and neglecting air resistance, the vertical displacement of an object released from rest is given by y − y0 = 1/2gplanett2, where gplanet is the acceleration due to gravity on the planet. You measure t in seconds for several values of y − y0 in meters and plot your data with t2 on the vertical axis and y − y0 on the horizontal axis. Your data is fit closely by a straight line that has slope 0.300 s2/m. Based on your data, what is the value of gplanet?arrow_forward
- An object's velocity as a function of time in one dimension is given by the expression; v(t) = 2.71t + 7.88 where are constants have proper SI Units. What is the object's velocity at t = 4.19 s?arrow_forwardSolving equations of motion Given an acceleration vector,initial velocity ⟨u0, v0, w0⟩, and initial position ⟨x0, y0, z0⟩, find thevelocity and position vectors, for t ≥ 0. a(t) = ⟨sin t, cos t, 1⟩, ⟨u0, v0, w0⟩ = ⟨0, 2, 0⟩,⟨x0, y0, z0⟩ = ⟨0, 0, 0⟩arrow_forwardA particle starts from the origin of a three-dimensional coordinate system and undergoes two consecutive displacements: r1→=2.0miˆ+1.0mjˆ+3.0mkˆr2→=−1.0miˆ−3.0mjˆ−1.0mkˆr1→=2.0mi^+1.0mj^+3.0mk^r2→=−1.0mi^−3.0mj^−1.0mk^ What is the distance of the particle from the origin after these two displacements?arrow_forward
- “An object is moving at a speed of v(t)= 3(t^2-1)+5tan (7t), where V is in m / s and t in seconds. What is your acceleration during the first two seconds? To answer this question, in mathematical terms, what are you asked to calculate an integral, a derivative, or a rate of change?arrow_forwardA space shuttle’s coordinates as functions of time are given by x(t) = 7.0 t^3 and y(t) = 4.0t^2 - 2.1t , where x and y are in meters and t is in seconds. write a vector expression for the ball's acceleration as a function of time.arrow_forwardGiven vector A = <2, -5, -24> and vector B = <6, 15, 20> , what is the magnitude of A x B?arrow_forward
- Classical Dynamics of Particles and SystemsPhysicsISBN:9780534408961Author:Stephen T. Thornton, Jerry B. MarionPublisher:Cengage LearningPrinciples of Physics: A Calculus-Based TextPhysicsISBN:9781133104261Author:Raymond A. Serway, John W. JewettPublisher:Cengage LearningCollege PhysicsPhysicsISBN:9781285737027Author:Raymond A. Serway, Chris VuillePublisher:Cengage Learning