. A particle has an initial position vector r=0 and an initial velocity v0=3i +2j(where distance is measured in meters and velocity in meters per second).The particle moves with a constant acceleration a=i -4j(measured in m/s2).At what time does the particle reach a maximum y coordinate? What is the position vector of the particle at that time?
. A particle has an initial position vector r=0 and an initial velocity v0=3i +2j(where distance...
4. A particle starts from an initial position with coordinates To = 8 + 5ſm, at time t= 0, with a velocity of V. = 3i-8 m/s. The particle moves in the r-y plane with a constant acceleration, à = -21 - m/s. (a) At the instant the y-coordinate of the particle's position is -10 m, find the x- coordinate of its position. (b) Calculate the x- and y-components of the particle's position when the particle reaches its turning point...
Suppose that the position vector of a particle is given by the following function of time: r = (6.0 + 2.0t^2)i + (3.0 - 2.0t + 3.0t^2)j where distance is measured in meters and time in seconds. (a) What is the instantaneous velocity vector at t=2.0 s? What is the magnitude of this vector? (b) What is the instantaneous acceleration vector? What are the magnitude and direction of this vector?
The vector position of a particle varies in time according to the expression r = 8.20 i-5.60p j where r is in meters and t is in seconds. (a) Find an expression for the velocity of the particle as a function of time. (Use any variable or symbol stated above as necessary.) x m/s Determine the acceleration of the particle as a function of time. (Use any variable or symbol stated above as necessary.) X m/s2 (c) Calculate the particle's...
Student Name 1. A particle confined to motion along the x axis moves with constant acceleration fromx = 2.0 m to x 8.0 m during a 2.5-s time interval. The velocity of the particle at x - 8.0 m is 2.8 m/s. What is the acceleration during this time interval? 2. The polar coordinates of a point are r=5.50 m and Angle 240°. What are the Cartesian coordinates of this point? 3. On occasion, the notation A= [A, O] will...
A particle leaves the origin with an initial velocity = (6.93) = 6.931 m/s and a constant acceleration (-- - 4.601 – 1.87j m/s2 When the particle reaches its maximum x coordinate, what are (a) its velocity, (b) its position vector? (a) Number Units (b) Number + Units
1. The position of a particle is described as r=xi+yj, where i and j are the coordinate unit vectors in 2D Cartesian coordinates a?d x and y are the coordinates of a particle. The velocity can be calculated as v=dr/dt. Find an expression for v, by taking the derivative of r with respect to time. 2. a=2.00 t, where t is the time, in seconds, and a is the acceleration in meters per second squared. s=0 and v=0 at t=0....
The vector position of a particle varies in time according to the expression r with arrow = 7.40 î − 5.00t2 ĵ where r with arrow is in meters and t is in seconds. (a) Find an expression for the velocity of the particle as a function of time. (Use any variable or symbol stated above as necessary.) v with arrow = m/s (b) Determine the acceleration of the particle as a function of time. (Use any variable or symbol...
Find the position vector for a particle with acceleration, initial velocity, and initial position given below. a(t) (4t, 2 sin(t), cos(2t)) 5(0) (0, 5,5) r(t) Preview Preview Preview The position of an object at time t is given by the parametric equations Find the horizontal velocity, the vertical velocity, and the speed at the moment wheret - 4. Do not worry about units in this problem. Horizontal Velocity - Preview Vertical Velocity- Preview Preview peed- Find the position vector for...
The vector position of a particle varies in time according to the expression r-7.40 i-8.20t2 j where r is in meters and t is in seconds. (a) Find an expression for the velocity of the particle as a function of time. (Use any variable or symbol stated above as necessary.) m/s (b) Determine the acceleration of the particle as a function of time. (Use any variable or symbol stated above as necessary.) m/s2 (c) Calculate the particle's position and velocity...
The acceleration of a particle is given by a = 12(10 – s)-2 m/s2 where s is in meters as it moves along a straight line. If the particle’s initial velocity is v0 = 4 m/s and its initial position is s0 = 2 m, determine the velocity of the particle at s = 8 m. Ans: 5 m/s