A particle describes an UCM(uniform circular motion) with period 0.500 s and circle centered at the origin of the x and y coordinate system. Let î and ȷ be the unit vectors along the x and y directions, respectively. At instant t=0 the particle's acceleration vector (in m/s2) is a =2.30î. What is its acceleration vector (in m/s2) at time t=2.50 s?

Q: A runner runs along the helix r(t) = (cost,sin t,t). When he isat position r( π/2), his speed is 3…

A: To find the acceleration vector

Q: 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…

A:

Q: A particle starts moving from the origin at time t = 0 with the dot production of the position…

A: 1.   Let us assume the position vector is represented by   r→=xi^+yj^and the velocity vectorv→=vx…

Q: A remote-controlled car is moving around in a level (horizontal) parking lot. The velocity of the…

A:

Q: A particle moves horizontally in uniform circular motion, over a horizontal xy plane. At one…

A: Given at coordinates (3.20m,4.60m)  velocity v=-4.40i^m/s acceleration a=+10.4j^m/s2 to find x and y…

Q: A particle travels clockwise around a circular path as shown below. The speed of the particle is…

A: See below

Q: A particle undergoes uniform circular motion in the x-y plane. At an instant in time its position is…

A: The position vector of the particle at a certain time  r→=1 i+2 jThe velocity of the particle,…

Q: At t;= 4.00 s, the acceleration of a particle moving at constant speed in counterclockwise circular…

A:

Q: The eguation r(t)= (3t+ 9) i + (8t - 2) j+(4t) k is the position of a particle in space at time t.…

A: Introduction: Kinematics helps to find out the velocity, acceleration of the particle at any time t…

Q: The position of a particle in space at time tis: r(t) = (sec(t)) * i + (tan t) * j + 4/3 tk. Write…

A: Given: The position of the particle is  rt=secti+tantj+43tk…

Q: A у -plane a velocity given by 2.4 m/s, B = 1.6 m/s³ and y = 4.0 m/s². The positive y -direction is…

A: Solution:

Q: The velocity of a particle is given by v = {16t²i + 4t³j + (5t +2)k}m/s, where t is in seconds. If…

A:

Q: A particle executes a motion on a circular path with a constant speed of 2 m/s. Using…

A: In a uniform cicular motion, the velocity of the particle is always tangential to the circle of…

Q: 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…

A:

Q: A particle moves in a circular path according to the clockwise equation θ(t)=π/4+2t−4t2, where θ is…

A: A particle moves in a circular path then acceleration is acting towards the center. Each and every…

Q: The coordinates of a particle moving in the XY plane are given as function of time by: X = 5m + (7…

A:

Q: A human archer atop a castle wall shoots an arrow at a velocity of 65 m/s at an angle of 36.9…

A: Launch velocity (u) = 65 msLaunch angle (θ) = 36.9o above the horizontal Time of flight (t) = 5.82…

Q: You stand at the edge of a 22.0 m high cliff and throw a stone straight down with a speed of 8.00…

A: Initial velocity, u = 8 m/sFinal velocity, v = 22.3 m/s

Q: 3. A particle moves according to the position vector F(t) = cos ti+ sin 3t j+ 2t k, where the…

A:

Q: A particle travels along the circular path 2. x² + y² = r².If the y component of the particle's…

A:

Q: A purse at radius 1.90 m and a wallet at radius 2.85 m travel in uniform circular motion on the…

A: Given that, A purse and a wallet are moving in a uniform circular path on the same radial line,…

Q: A particle is in uniform circular motion about the origin of an xy coordinate system, moving…

A:

Q: A particle has a position function r ⃗ (t) = cos(1.0t)i ^ + sin(1.0t)j ^ + tk ^ , where the…

A: The Velocity vector is defined as the rate of change of position vector with respect to time and the…

Q: A student standing on a cliff that is a vertical height d = 8.0 m above the level ground throws a…

A:

Q: A particle moves along a circular path over a horizontal xy coordinate system, at constant speed. At…

A:

Q: At time t = 0, a particle is located at the point (1,3,8). It travels in a straight line to the…

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Q: A rocket starts at rest on a launchpad.  At t = 0 the rocket has a constant acceleration of a= 25…

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Q: A particle r = (2t3+ 3t) i + (4 - 5t2) j - t4 k Position depending on time given position moves with…

A: Given quantities: position vector (r) = ( 2t3 + 3t ) i + ( 4 - 5t2 ) j - t4 k   Let, the distance…

Q: A particle moves along in three-dimensional motion with position vector given x (t) = 3.20 t m i +…

A: The physical quantities are of two types- scalar and vector quantities. The scalar quantities are…

Q: A student standing on a cliff that is a vertical height d = 8.0 m above the level ground throws a…

A: According to the kinematics equation of motion along y axis,…

Q: A Particle is in the xy-plane in uniform circular motion around the origin. The x- and y-…

A:

Q: Problem 2: An object rolls off a tabletop with a horizontal velocity vox = 12 m/s. The table is at a…

A: a) Consider vertical motion    Sy=So+uyt+12ay.t2   0 = -1.7+ot+12x9.81t2   1.7=12x9.81xt2…

Q: At time t = 0 a particle at the origin of an xyz-coordinate system has a velocity vector of Vo =i+…

A:

Q: acceleration of the wallet?

A: Given: Radius of circle in which purse is placed, is rp=2.20 m Radius of circle in which wallet is…

Q: The coordinates of a bee flying in the xy-plane are given by x(t) = At and y(t) = C-Bt², where 1 =…

A: Given: The coordinate of the bee in the xy plane is.  xt=At…

Scalars and Vectors

Scalars and Vectors are the classification of physical quantities that are used to denote various terms in physics.