A particle travels along the circular path x² + y² = r². If the y component of the particle's velocity is v, = 2r cos 2t, determine the x and y components of its acceleration at any instant.
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- Figure OQ3.3 shows a birds-eye view of a car going around a highway curve. As the car moves from point 1 to point 2, its speed doubles. Which of the vectors (a) through (e) shows the direction of the cars average acceleration between these two points?At t = 0, a particle moving in the xy plane with constant acceleration has a velocity of vi=(3.00i2.00j)m/s and is at the origin. At t = 3.00 s, the particles velocity is vf=(9.00i+7.00j)m/s. Find (a) the acceleration of the particle and (b) its coordinates at any time t.A particle moves horizontally in uniform circular motion, over a horizontal xy plane. At one instant, it moves through the point at coordinates (4.00 m, 4.00 m) with a velocity of -5.00 m/s i and an acceleration of -12.5 (m/s^2) j . What are the (a) x and (b) y coordinates of the center of the circular path?
- A particle is moving along a circular path of 2-m radius such that its position as a function of time is given by theta = (5t^2) rad, where t is in seconds. Determine the magnitude of the particle’s acceleration when theta = 30°. The particle starts from rest when u = 0°.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?A particle moves horizontally in uniform circular motion, over a horizontal xy plane. At one instant, it moves through the point at coordinates ( 4.80 m, 4.00 m) with a velocity of – 3.50 i^ m/s and an acceleration of + 10.9 j^ m/s2. What are the (a) x and (b) y coordinates of the center of the circular path?
- A particle moves along a circular path over a horizontal xy coordinate system, at constant speed.At time t1 = 4.00 s, it is at point (5.00 m, 6.00 m) with velocity (3.00 m/s) and acceleration in the positive x direction. At time t2 10.0 s, it has velocity ( 3.00 m/s) and acceleration in the positive y direction.What are the (a) x and (b) y coordinates of the center of the circular path if t2 - t1 is less than one period?A particle moves along a circular path over a horizontal xy coordinate system, at constant speed. At time t1 = 3.30 s, it is at point (4.40 m, 5.90 m) with velocity (2.70 m/s)ĵ and acceleration in the positive x direction. At time t2 = 12.0 s, it has velocity (–2.70 m/s)î and acceleration in the positive y direction. What are the (a) x and (b) y coordinates of the center of the circular path? Assume at both times that the particle is on the same orbit.A particle moves in the xy plane in a circle centered at the origin. At a certain instant the velocity and acceleration of the particle are 6.0i m / s and (3.0i + 4.0j) m / s2 respectively. What are the x and y coordinates of the particle at this time?
- A particle travels around a circular path having a radius of 50 m. If it is initiallytraveling with a speed of 10 m/s and its speed then increases at a rate of a (v) = (0.05v) m/s 2 , thendetermine the magnitude of the particle’s acceleration four seconds later.From the origin, a particle starts at t = 0 s with a velocity vecv=7.0hatim/s and moves in the xy plane with a constant acceleration of a=(-9.0hati+3.0hatj)m/s^(2). At the time the particle reaches the maximum x coordinate, what is its (a) velocity and (b) position vector?A particle is moving in a circular path with v = 8t m/s, where "t" is in seconds. If the circumference of the path is 9π cm. Find the magnitude of its total acceleration at time = 4 s.