Problem #2: The position of a particle moving along the x-axis is given by x(t) = 3t-12t (a) When does the particle cross the origin? (b) What is the displacement of the particle from t=2s to t-6s? (c) What is the velocity at t-5s?
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- In the figure, particle A moves along the line y = 31 m with a constant velocity of magnitude 2.7 m/s and parallel to the x axis. At the instant particle A passes the y axis, particle B leaves the origin with zero initial speed and constant acceleration of magnitude 0.48 m/s2. What angle ? between and the positive direction of the y axis would result in a collision?The velocity of a particle is given by v ={16t^2i +4t^3j + (5t +2)k} m/s, where t is in seconds. If the particle is at the origin when t = 0, determine the magnitude of the particle’s acceleration when t = 2 s. Also, what is the x, y, z coordinate position of the particle at this instant?A particle moves along xy-plane with a position of a (t) = sin(2t) + 3 cos(4t) y (t) = sin(t) – 6 cos(3t) = a Determine the position vector of the particle b. Determine the velocity vector of the particle c Determine the acceleration vector of the particle d Determine the position vector of the particle when I - 4 e Determine the average acceleration from t -0s to t- 5s f Determine the instantaneous acceleration when - is g Determine the average velocity from t- Is tot 3s
- A child running in a field has the following position and velocity at time t=0: x = 1.5 m. v= -2.0 m. Vx =-3.5 m/s, vy = 1.0 m/s At time t = 2.5 s, it has the following position and velocitv: x = -1.0 m, y = 1.5 m 08. Vx = -0.50 m/s, Vy = 2.0 m/s Using this information, find the magnitude and direction of the child's…If an object is thrown horizontally with an average x-component of its velocity equal to 5 m/s, and does not hit the ground, what will be the x-component of the displacement after 20s?A particle leaves the origin with initial velocity v0= 12i + 14j m/s, undergoing constant acceleration a = -0.80i + 0.25j m/s2. If the particle crosses the y-axis at t = 30s and its y-coordinate at the time is 532.5m. How fast is it moving and in what direction is it moving?
- A marble is launched from the edge of a table at a angle of 45 ° up from horizontal and goes through the air until it hits the floor. True or False? For such a marble, |vx| (the magnitude of the x-component of the velocity) is decreasing the entire time the marble is airborne.A projectile is launched with a launch angle of 30° with respect to the horizontal direction and with an initial speed of 26 m/s. How do the vertical and horizontal components of the projectile's velocity vary with time?The initial velocity in the x-direction vx0 is related to the initial speed by vx0 = v0 cos 30°. The constant velocity in the x-direction means that the equation describing the time dependence of x for the particle, with x0 taken as 0, is x = x0 + vx0t = 0 + m/s t. The equation for the vertical coordinate, which is constantly accelerating downward at g = 9.8 m/s2, is y = y0 + vy0t − 1 2 gt2 = m/s t + m/s2 t2.The acceleration vector of a particle is giving by a = -27 t2 j m/s4. The particle is located at the origin at t = 0 s and has an initial velocity Vo = 2(m/s) i + 3(m/s) j. Find: a) The velocity of the particle as a function of time. b) The maximum height the particle reaches.
- The acceleration of a particle at any time t ≥ 0 is given by a = 12 ti + 9sin3tj + 9cos3tkIf the velocity v and displacement r are zero at t= 0, find r at any time t.A particle starts from the origin at t=0, with an initial velocity having an x component of 20m/s and a y component of -15m/s. The particle moves in the xy plane with an x component of acceleration only, given by Ax =4.0 m/s^2 Determine the components of the velocity vector at anytime and the total velocity vector at any time . Calculate the velocity and speed of the particle at t=5.0s.A particle moves along xy-plane with a position of x (t) = sin(2t) + 3 cos(4t) y (t) = 1/2 sin(t) – 6 cos(3t) a. Determine the position vector of the particle when t = 4s. b. Determine the average acceleration from t = 0s to t= 5s. c. Determine the instantaneous acceleration when t= 1s. d. Determine the average velocity from t= 1s to t= 3s.