The particle’s position vector varies in time according to the expression ?= 3.00i − 6.00t2? ? (a) Determine the particle’s position and velocity at t = 1.00 s.
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The particle’s position vector varies in time according to the expression ?= 3.00i − 6.00t2? ? (a) Determine the particle’s position and velocity at t = 1.00 s.
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- Figure OQ3.3 shows a birds-eye view of a car going around a highway curve. As the car moves from point 1 to point 2, its speed doubles. Which of the vectors (a) through (e) shows the direction of the cars average acceleration between these two points?From the origin, a particle starts at t = 0 s with a velocity vecv=7.0hatim//s and moves in the xy plane with a constant acceleration of veca=(-9.0hati+3.0hatj)m//s^(2). At the time the particle reaches the maximum x coordinate, what is its (a) velocity and (b) position vector?The position vector 7 = (4.30t)î + (et + ft²) locates a particle as a function of time t. Vector is in meters, t is in seconds, and factors e and fare constants. The figure gives the angle of the particle's direction of travel as a function of time (0 is measured from the positive direction of the x axis). What are (a) factor e and (b) factor f, including units? 20° 0° -20° 10 t(s) 20
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- The position vector of a particle is r(t). Find the requested vector. 1. The velocity at t = pi/4 for r(t) = 2sec2(t) i - 6tan(t) j + 4t2 k. 2. The acceleration at t = 3 for r(t) = (5t - 2t4) i + (9 - t) j + (8t2 - 9) k.The displacement vectors A and B shown in Figure P3.9 both have magnitudes of 3.00 m, The direction of vector A is 0 = 30.0°. Find graphically 9. (a) +B, Answer + (b) A - B, Answer + (c) B - 7, and Answer + (d) A- 2B. (Report all angles counterclockwise from the positive = axis.) Figure P3.9 Problems 9 and 25.A particle moves in the x-y plane with constant acceleration. At time t = 0 s, the position vector for the particle is d = 5.8 m x + 2.1 m y. The acceleration is given by the vector a = 8.3 m/s2 x + 7.8 m/s2 y. The velocity vector at time t = 0 s is v = 5.3 m/s x - 7.5 m/s y. Find the magnitude of the velocity vector at time t = 7.5 s. What is the angle between the velocity vector and the positive x-axis at time t = 7.5 s? What is the magnitude of the position vector at time t = 7.5 s? What is the angle between the position vector and the positive x-axis at time t = 7.5 s?
- The velocity of a particle is V and is constant. It moves counterclockwise on a circle with center "O" and radius R. Draw the circle. When the particle is in the vector R position, draw vector R, vector V, vector A, and vector da/dt(time derivative of acceleration).A particle has a position function r ⃗ (t) = cos(1.0t)i ^ + sin(1.0t)j ^ + tk ^ , where the arguments of the cosine and sine functions are in radians. (a) What is the velocity vector? (b) What is the acceleration vector?The figure shows the path taken by a drunk skunk over level ground, from initial point i to final point f. The angles are 9-26.0% 8₂-49.0% and 6-76.0°, and the distances are d₁ - 5.90 m, d₂-7.40 m. and da = 12.0 m. What are the (al magnitude and (b) angle of the skunk's displacement from i to f? Give the angle as a positive (counterclockwise) or negative (clockwise) angle of magnitude less than 180°, measured from the +x direction. Units (a) Number Units (b) Number i