Particle originally at rest and located at (0.9m, 0.6m, 1.5m) is subjected to an acceleration of a (6t i+ 12t2 k) m/s?. Determine (a) The velocity vector, and (b) The position (x, y, z) at t = 1 s

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) : c = 0.120 m/s², and d = 1.02 m. (a) Calculate the average velocity during the time interval from t = 2.10 s to t = 3.85 s. V = m/s (b) Determine the velocity at t = 2.10 s. m/s = at + b and y(t) = ct² + d, where a = 1.80 m/s, b = Determine the speed at t = 2.10 s. m/s 1.20 m,

The figure shows the y-position (in blue) of a particle versus time. y (m) 20 16 12 Need Help? 8 4 0 1 2 3 4 (a) What is the average velocity of the particle during the time interval t = 0.50 s to t = 4.50 s? (Express your answer in vector form.) m/s m/s 5 (b) Using the tangent to the curve (shown as the orange line in the figure), what is the instantaneous velocity of the particle at t = 1.50 s? (Express your answer in vector form.) -t (s) Read It (c) At what time is the velocity of the particle equal to zero? S

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A particle initially located at the origin has an acceleration of a = 1.00j m/s? and an initial velocity of v = 6.00î m/s. (a) Find the vector position of the particle at any time t (where t is measured in seconds). ( 6 tî+ +5 t? j) m (b) Find the velocity of the particle at any time t. (6 î + 1 v tj) m/s (c) Find the coordinates of the particle at t = 6.00 s. X = 36 m y = 0 For the y coordinate of the particle, you need to know the y components of the initial position, the velocity, and the acceleration. m (d) Find the speed of the particle at t = 6.00 s. 8.49 m/s

A particle leaves the origin with an initial velocity 3.00î m/s and a constant acceleration ở -1.00î – 0.50ĵ m/s². When it reaches its maximum x coordinate, what are its (a) velocity and (b) position vector?

A proton initially has 7 = (-7.10)î + (5.10)Ƒ + (−6.60)î : and then 2.70 s later has 7 = (4.70)î + (5.10)ĵ + (13.0)ê (in avg meters per second). (a) For that 2.70 s, what is the proton's average acceleration a in unit vector notation, (b) in magnitude, and the angle between a and the positive direction of the x axis? avg (a) Number i 11.8 (b) Number i (c) Number i î+ Units Units i 19.6 k Units m/s

Number An ion's position vector is initially 7 = (2.4 m )î + (−7.4 m )3 + (6.5 m ). In unit-vector notation, what is its average velocity during the 6.7 s? )ĵ i 1 + = 9.1 m )i + (−9.9 m )ĵ + (−10 m )k, ) + (-10 m ), and 6.7 s later it is -0.37313433 Ĵ + MI -2.46268657 k Units m/s

Question 2: The acceleration function of an object doing curvilinear motion is a = {(-0.2t)i+4j+1.5k} m/s², where t is in s. If its initial velocity vo = 8i m/s, and initial position is at the origin, determine the magnitude of its position when t = 3 s. (а) 25.7 m (b) 38.9 m (с) 62.3 m (d) 22.1 m

An ion's position vector is initially r→=(-3.7m)î+(-6.4m)ĵ+(9.3m)k̂, and 9.4 s later it is r→=(8.3m)î+(5.0m)ĵ+(8.2m)k̂. In unit-vector notation, what is its average velocity during the 9.4 s?