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2. A particle is moving horizontally from an initial position Xo = 0, with an initial...
Find the position function x(t) of a moving particle with the given acceleration a(t), initial position Xo = x(0), and initial velocity vo = v(O). a(t) = 4(t+3)2, v(0) = - 4, x(0) = 2
1. (10 pts) A particle moving along a straight line decelerates according to a -kv. This represents a drag-induced deceleration. Determine: a) velocity v as a function of time t b) position s as a function of time t c) velocity v as a function of position s At time t-0, the initial velocity is vo and position is s 0
7. A body of mass m-1kg initially is at position xo- -1m and starts moving away from the origin with speed to = 10m/sec. It is moving along the z axis under the influence of three forces (i) an attractive force towards the origin which is 8 times the position of the body (ii) the air resistance which is 6 times the velocity of the body; 160 (iii) and the kinetic friction with coefficient μ (a) The initial value problem...
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...
feet per second and in miles per second 18 An object of mass m is moving horizontally through a medium which resists the motion with a force that is a func- tion of the velocity; that is, d's dv f(v) dt =m dt2 where v = s(1) represent the velocity and at time , respectively. For example, v(t) and s position of the object think of a boat moving through the water. (a) Suppose that the resisting force is proportional...
The position of a particle moving along an x axis is given by x = 14.0t^2 - 5.00t^3, where x is in meters and t is in seconds. Determine the position, the velocity, and the acceleration of the particle at t = 6.00 s. What is the maximum positive coordinate reached by the particle and at what time is it reached? What is the maximum positive velocity reached by the particle and at what time is it reached? What is...
2 A particle falling from rest in a vertical line in a medium with resistance kv per unit mass, k is a constant, v is the velocity at any time and position x, prove that it acquires a speed 9. -2kh 1 - e T is the terminal velocity given by a distance h, where in falling through T A particle projected upwards in the same medium with initial speed V, and returns to the point of projection with speed...
* A particle is moving with acceleration function a(t) = 21-1, find the position of the object where the initial velocity is v(O)=2 and the initial position is s(0)=1. a. -3 -2 +21 b.sin(2x) OC 12 +2 Od. - *+21+1 Oe 12-*+2+1
Find the position vector for a particle with acceleration, initial velocity, and initial position given below. a(t) = (2+, 4 sin(t), cos(5t)) v(0) = (-3, -5,0) 7(0) = (-5,2, - 1) F(t)
The acceleration function (in m/s2) and the initial velocity v(o) are given for a particle moving along a line. a(t) = 2t + 2, VO) = -15, Osts 5 (a) Find the velocity at time t. v(t) = m/s (b) Find the distance traveled during the given time interval.