The position vector of a particle changes with time according to the relation 7(t) = 15t2 î + (4 – 20t2)ĵ. What is the magnitude of the acceleration at t = 1?
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- A particle initially located at the origin has an acceleration of a=3.00jm/s2 and an initial velocity of vi=5.00im/s. Find (a) the vector position of the particle at any time t, (b) the velocity of the particle at any time t, (c) the coordinates of the particle at t = 2.00 s, and (d) the speed of the particle at t = 2.00 s.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?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 time
- 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).Find the position vector of a particle whose acceleration vector is a=(6t,2) with an initial velocity vector (0,0) and initial position vector (3,0).At what times in the interval 0 ≤ t ≤ π are the velocity and acceleration vectors of the motion r(t) = i + (5 cos t)j + (3 sin t)k orthogonal?
- A particle is at rest and at x=0 and y=0 at time = 0. The particle then moves in the x-y plane with an acceleration in m/s^2 of a = 5t^2 i + 5t j , where t is in seconds. Determine the magnitude of the particle's position vector in m at instant the x-component of the velocity vector vx = 8 m/s.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.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
- As a projectile moves in its path, is there any point along the path where the velocity and acceleration vectors are (a) perpendicular to each other? (b) Parallel to each other?Answer the problem by choosing one of the eight labeled acceleration vectors or selecting option I: a→ = 0→. At this instant, the particle has steady speed and is curving to the right. What is the direction of its acceleration?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).