At time t = 0, the position vector of a particle moving in the x-y plane is r = 5.80i m. By time t = 0.016 s, its position vector has become (6.08i + 0.42j) m. Determine the magnitude vay of its average velocity during this interval and the angle made by the average velocity with the positive x-axis. Answers: m/s Vav 0= i
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- At t = 0, a particle moving in the xy plane with constant acceleration has a velocity of vi=(3.00i2.00j)m/s and is at the origin. At t = 3.00 s, the particles velocity is vf=(9.00i+7.00j)m/s. Find (a) the acceleration of the particle and (b) its coordinates at any time t.A motorist drives south at 20.0 m/s for 3.00 min, then turns west and travels at 25.0 m/s for 2.00 min, and finally travels northwest at 30.0 m/s for 1.00 min. For this 6.00-min trip, find (a) the total vector displacement, (b) the average speed, and (c) the average velocity. Let the positive x axis point east.The vector position of a particle varies in time according to the expression r (3.00i 6.00t 2 j) m. (a) Findexpressions for the velocity and acceleration as functions of time. (b) Determine the particle’s position andvelocity at t 1.00 s
- The position r→ of a particle moving in an xy plane is given by r→=(3.00t^3−7.00t)i^+(6.00−2.00t^4)j^ with r→ in meters and t in seconds. In unit-vector notation, calculate(a)r→, (b)v→, and (c)a→ for t = 2.00 s. (d) What is the angle between the positive direction of the x axis and a line tangent to the particle's path at t = 2.00 s? Give your answer in the range of (-180o; 180o).A particle initially located at the origin has an acceleration of = 2.00ĵ m/s2 and an initial velocity of i = 9.00î m/s. (a) Find the vector position of the particle at any time t (where t is measured in seconds).( t î + t2 ĵ) m(b) Find the velocity of the particle at any time t.( î + t ĵ) m/s(c) Find the coordinates of the particle at t = 3.00 s.x = my = m(d) Find the speed of the particle at t = 3.00 s. m/sSolving 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⟩
- A particle initially located at the origin has an acceleration of = 4.00ĵ m/s2 and an initial velocity of i = 6.00î m/s. (a) Find the vector position of the particle at any time t (where t is measured in seconds).( t î + t2 ĵ) m(b) Find the velocity of the particle at any time t.( î + t ĵ) m/s(c) Find the coordinates of the particle at t = 7.00 s.x = my = m(d) Find the speed of the particle at t = 7.00 s.m/sA particle initially located at the origin has an acceleration of = 1.00ĵ m/s2 and an initial velocity of i = 9.00î m/s. (a) Find the vector position of the particle at any time t (where t is measured in seconds). (b) Find the velocity of the particle at any time t. (c) Find the coordinates of the particle at t = 3.00 s. (d) Find the speed of the particle at t = 3.00 s.The positionr→of a particle moving in an xy plane is given byr→=(5.00t3−6.00t)i^+(2.00−2.00t4)j^withr→in meters and t in seconds. In unit-vector notation, calculate(a)r→, (b)v→, and (c)a→for t = 2.00 s. (d) What is the angle between the positive direction of the x axis and a line tangent to the particle's path at t = 2.00 s? Give your answer in the range of (-180o; 180o).
- A particle starts from the origin at t=0, with an initial velocity having an x component of 20m/s and a y component of -15m/s. The particle moves in the xy plane with an x component of acceleration only, given by Ax =4.0 m/s^2 Determine the components of the velocity vector at anytime and the total velocity vector at any time . Calculate the velocity and speed of the particle at t=5.0s.On 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.A fish swimming in a horizontal plane has velocity i = (4.00 î + 1.00 ĵ) m/s at a point in the ocean where the position relative to a certain rock is i = (12.0 î − 2.60 ĵ) m. After the fish swims with constant acceleration for 15.0 s, its velocity is = (25.0 î − 1.00 ĵ) m/s. (a) What are the components of the acceleration of the fish? ax = ay = (b) What is the direction of its acceleration with respect to unit vector î? Draw coordinate axes on a separate piece of paper, and then add the acceleration vector with its tail at the origin. Write the numerical values for the x and y components and then use this drawing to determine the angle.° counterclockwise from the +x-axis(c) If the fish maintains constant acceleration, where is it at t = 28.0 s? x = m y = m In what direction is it moving? ° counterclockwise from the +x-axis