The velocity of a particle moving in thex-y plane is given by (4.03i + 7.36j) m/s at time t = 3.64 s. Its average acceleration during the next 0.020 s is (2.2i + 2.6j) m/s?. Determine the velocity v of the particle at t = 3.660 s and the angle e between the average- acceleration vector and the velocity vector at t = 3.660 s. Answers: v= ( i i+ i j) m/s e =
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- The acceleration of a particle moving only on a horizontal xy plane is given by d = 6tî + 7tj, where d is in meters per second-squared and tis in seconds. At t= 0, the position vector 7 = (15.0m)î + (35.0m)ĵ locates the paticle, which then has the velocity vector V = (6.40m/s)î + (3.30m/s)ĵ. At t = 5.60 s, what are (a) its position vector in unit-vector notation and %3D (b) the angle between its direction of travel and the positive direction of the x axis? (a) Number i j Units i (b) Number i UnitsSuppose that a particle begins its motion from the origin and meets the velocity (in m / s) given by: vx (t) = 2.50t vy (t) = 3.50√t. for t> 0 in seconds. Find the speed of the particle at t = 5.00 s What is the acceleration vector (in rectangular components) at t = 2.00 s ? Find the magnitude of the displacement between t = 0.00 s and t = 6.00 sInitially, a bicycle is at the position r= (130 mji + (210 m)j - After 120 s. the postion of the particle is = (110 mmi + (240 m)j What is the average velocity vector of the bicycle in ihat time tinterval? O Tav = (-0.17 m/s)i + (0.25 m/s); O Tay = (0.25 m/s)i+(-0.17 m/s) O Tay = (0.17 m/s)î + (-0.25 m/s)j O Tay = (-0.25 m/s)i+ (0.17 m/s)ĵ
- A particle moving with an initial velocity v, = (10m/s)î and initial position 7, = (4m)î + (2m)j, undergoes an acceleration ở = 2t²î + 4ĵ in SI units. For t = 10 s; a) Calculate the velcoity v= vxI+ vy®. b) Calculate the position r= x+ y. c) What are the magnitudes of the velocity and the position vector of the particle? d) Find also the angle each vector is making with the x-axis at that time.the coordinates of an object moving in an xy plane vary with the time according to the eqations x=-7.85 sin w(omega)t, and y=4-7.85 cosw(omega)t. W(omega) is constant , x,y - in meters. And t in seconds. Write expressions for the possition,velocity and acceleration vectors of the object at any time t>0.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 acceleration of a particle moving only on a horizontal xy plane is given by a = 2tî + 31ĵ, where a is in meters per second- squared and t is in seconds. At t = 0, the position vector = (23.0m)i + (47.0m) locates the paticle, which then has the velocity vector 7 = (6.40m/s)i + (3.20m/s) j. At t = 4.60 s, what are (a) its position vector in unit-vector notation and (b) the angle between its direction of travel and the positive direction of the x axis? (a) Number i (b) Number i î+ Units i ĴUnitsThe velocity i of a particle moving in the xy plane is given by 7 = ( 5.50 - 5.00 ji + 9.00 3. with V in meters per second and t (> 0) in seconds. At I- 1.40 s and in unit-vector notation, what are (a) the x component and (b) the y component of the Eceleratiun? (c) Whien(if uver) is the acceluration zero? (d) At wlat pusitive time does the speed equal 10.0 mh? (a) Numher 7 Unit (b) Number 1 Unit {c) Number Unit (d) Number UnitThe velocity vector of a particle is given by: V = Vje-)[sin(wt)i + cos(wt)j] where, Vo = 12.1 m/s; T = 2.5 s; w = 5.2 rad/s Calculate the magnitude of the acceleration (in m/s2) at t = 7.4 s
- At time t = 0 a particle at the origin of an xyz-coordinate system has a velocity vector of Vo =i+ 12j - k. The acceleration function of the particle is a(t) = 16ti+j+ (cos 2t)k. Find the speed of the particle at time t = 1. Round your answer to two decimal places. Speed =At time t = 0, the position vector of a particle moving in the x-y plane is r = 4.62i m. By time t = 0.011 s, its position vector has become (4.84i +0.54j) m. Determine the magnitude Vay of its average velocity during this interval and the angle 0 made by the average velocity with the positive x-axis. Answers: Vav 0= i i m/sA particle initially located at the origin has an acceleration of a = 1.00j m/s2 and an initial velocity of v; = 6.00î m/s. %3D (a) Find the vector position of the particle at any time t (where t is measured in seconds). tî + t2 j) m (b) Find the velocity of the particle at any time t. tj) m/s (c) Find the coordinates of the particle at t = 7.00 s. X = m y = m (d) Find the speed of the particle at t = 7.00 s.