What is the instantaneous acceleration of a particle at t = 0.56 s whose position vector is given by the function F= (2.1t²)î + (3.6t) j. Assume all quantities are in Sl units. O ā = (0.66 m/s³)î + (2.0 m/s²)ĵ (3.6 m/s?)} Oā = (4.2 m/s³)î Oā = (2.1 m/s )i + (3.6 m/s²)ĵ
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- 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 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 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).
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- 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.Suppose the position vector for a particle is given as a function of time by r(t) = x(t)î + y(t)ĵ, with x(t) = at + b and y(t) = ct2 + d, where a = 1.10 m/s, b = 1.25 m, c = 0.123 m/s2, and d = 1.02 m. (a) Calculate the average velocity during the time interval from t = 1.85 s to t = 3.85 s. (b) Determine the velocity and speed at t = 1.85 s.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 = (16.0 î − 3.20 ĵ) m. After the fish swims with constant acceleration for 15.0 s, its velocity is = (21.0 î − 6.00 ĵ) m/s. (a) What are the components of the acceleration of the fish? ax = m/s2 ay = m/s2 (b) What is the direction of its acceleration with respect to unit vector î? ° counterclockwise from the +x-axis(c) If the fish maintains constant acceleration, where is it at t = 30.0 s? x = m y = m In what direction is it moving? ° counterclockwise from the +x-axis