According to the given equations of motion of the particle M determine the type of trajectory and for a moment of time t=t_1, find its position on the trajectory, its velocity , total tangential and normal acceleration , and a radius of the trajectory curvature. a) X=-2t^2+3,(cm), Y=-5t(cm) , t_1=0.5(s)
b) X=-3/(t+2), Y=3t+6, t_1=2
According to the given equations of motion of the particle M determine the type of trajectory...
The equation of motion of a particle is described by: OM t-1+(2)1 Determine the equation of trajectory of the particle and plot it on an xy coordinate system. a) b) At which point the motion starts. c) Determine the velocity vector and the acceleration vector of the particle in function of t d) Determine the tangential acceleration, the normal acceleration, and the radius of curvature in function of t. Is this a central acceleration, why or why not? At what...
The motion of a particle is defined by the equations x = (2t + t?) m and y = (t2) m, where t is in seconds. Determine the normal and tangential components of the particle's velocity and acceleration when t = 2 s.
For a given law of motion of a particle M find a location of a particle for a time ty (in sec), trajectory, velocuty, tangential, normal and full acceleration -2t +3 4 cos (xt/3) 2 4 sin2(xt/3) sin(rt/3) -1 4t +4 2sin(t/3) 3e2 +2 3t2 + 7 sin(rt/6) +3 -3cos(nt/3) + 4 -141 1/2 2os(t/6) 4 cos(t/3) 10 83t 5 cos (t/6)-3 -5 sin rt2/3) 1/2 5 sin2(xt/6) 5 cos(rt2/3) -2t-2 412 13 14 4 cos(xt/3) 3sin(rt/3) 16 3t 1/2...
Please show all work and graph #13 Define an equation of path, position of particle M on path at t = ti (sec), velocity, normal, tangent and full accelerations of the particle M, radius of curvature at t = tį. The defined parameters show on the graph. ti, sec Equations of motion of particle M r=x(t), cm y=y(t), cm - 21² + 3 -5t 4t +4 t +1 2 sin cos 1 t + 4 - 3 -4t 313 +...
The motion of a particle is defined by the equations x = (2t + t?) m and y = (t2) m, where t is in seconds. Determine the normal and tangential components of the particle's velocity and acceleration when t = 2 s. Select one 0 a. Vt= 6.0 m/s. Vn= 4.0 m/s, at= 2.0 m/s2, an= 2.0 m/s2 b. Vt= 1.55 m/s. Vn= 6.2 m/s at= 5.3 m/s2 an= 3.2 m/s2 c. Vt= 5.3 m/s. Vn= 3.2 m/s at=...
A particle moves on x-y plane according to the equations x = a cos (wt), y = b sin (wt). 1 - Show that its trajectory is an ellipse? 2 - Calculate the values of its velocity v(t) = |v(t)| and acceleration a(t) = |a(t)| ? 3 - What are the maximal and minimal values of v(t) and a(t) ? I think for the first part the answer is as the following image. Please correct me if my answer is...
The equations of motion for a particle of mass m and electrical charge q under the influence of a uniform magnetic field B perpendicular to the plane of motion are mx" = qBy' and my" = -qBx'. where x and y are the horizontal Cartesian position coordinates of the particle. Suppose that the particle initially satisfies the conditions Solve the initial value problem and sketch out the trajectory of the particle for t Greaterthanorequalto 0.
1. The parametric equations of an object are given by x = Rcos(wt), and y-Ksin(ot), where x and y are measured in meters and t in seconds. Assume R and ω are known. Calculate the following: (a) The radius of curvature ρ when x = 0.5K meter. Do it by applying the formula ラク dxz (b) The magnitude of the velocity as function of time (c) The x and y components of the acceleration as function of time.( ax-a,-?) (d)...
3. A particle moving along the x axis in simple harmonic motion starts from its equilibrium position, the origin, at t=0 s and moves to the right. The amplitude of its motion is 2.00 cm, and the frequency is 1.50 Hz. (a) Determine the position, velocity, and acceleration equations for this particle. (b) Determine the maximum speed of this particle and the first time it reaches this speed after t=0 s.
In an engine, a piston oscillates with simple harmonic motion so that its position varies according to the expression, x = 6.00 cos (5t + where x is in centimeters and t is in seconds. (a) At t-0, find the position of the piston 5.40581 cm (b) At t-0, find velocity of the piston. 2.60 How do you find the velocity v(t) of an object if you know the position as a function of time, x(t)? cm/s (c) At t...