The position of a particle is defined by r = {20 cos;t i + 8 sin-t j} m, where t is in seconds and the arguments for the sine and cosine are given in radians. Determine the magnitudes of the velocity and acceleration of the particle when t = 3 s.
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- A particle moves horizontally in uniform circular motion, over a horizontal xy plane. At one instant, it moves through the point at coordinates (3.40 m, 3.10 m) with a velocity of -3.20 i m/s and an acceleration of +14.3 j m/s?. What are the (a) x and (b) y coordinates of the center of the circular path? (a) Number Unit (b) Number UnitA cat rides a merry-go-round turning with uniform circular motion. At time t = 1.70 s, the cat's velocity is (3.90 m/s) î + (2.50 m/s) ĵ, measured on a horizontal xy coordinate system. At t2 = 5.30 s, its velocity is (-3.90 m/s) î + (-2.50) ĵ. What are (a) the magnitude of the cat's centripetal acceleration and (b) the magnitude of the cat's average acceleration during the time interval t2 - t1, which is less than a %3D period of the motion? (a) Number Unit (b) Number Unit >The best leaper in the animal kingdom is the puma, which can jump to a height of 12.7 ft when leaving the ground at an angle of 50°. With what speed, in SI units, must the animal leave the ground to reach that height?
- At t=0 a particle leaves the origin with a velocity of 5 m/s in the positive y direction. It's acceleration is given by a=(3i-2j)m/s^2 .at the instant the particle reaches its maximum y coordinate how far is the particle from the origin?A particle moves horizontally in uniform circular motion, over a horizontal xy plane. At one instant, it moves through the point at coordinates (3.70 m, 4.10m) with a velocity of -2.70 7 m/s and an acceleration of +12.9 m/s². What are the (a) x and (b) y coordinates of the center of the circular path? (a) Number i (b) Number i Unit UnitA 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 initially located at the origin has an acceleration of a = 1.00ĵ m/s2 and an initial velocity of ₁ = 6.00î m/s. (a) Find the vector position of the particle at any time t (where t is measured in seconds). tî + t²ĵ) m (b) Find the velocity of the particle at any time t. Î+ tĵ) m/s (c) Find the coordinates of the particle at t = 4.00 s. X = y = m m (d) Find the speed of the particle at t = 4.00 s. m/sPlease asapThe position vector 4.70t|i+ [et + ft2 locates a particle as a function of time t. Vector is in meters, t is in seconds, and factors e and f are constants. The figure gives the angle e of the particle's direction of travel as a function of time (0 is measured from the positive direction of the x axis). What are (a) factor e and (b) factor f, including units? 20° 0° 10 20 -20° t (s) (a) Number Units (b) Number Units
- The position of a particle is described byr = (t3+ 4t –4) m and θ = (t3/2) rad, where t is inseconds. Determine the magnitudes of the particle’svelocity and acceleration at the instant t = 2 s.Number An ion's position vector is initially 7 = (2.4 m )î + (−7.4 m )3 + (6.5 m ). In unit-vector notation, what is its average velocity during the 6.7 s? )ĵ i 1 + = 9.1 m )i + (−9.9 m )ĵ + (−10 m )k, ) + (-10 m ), and 6.7 s later it is -0.37313433 Ĵ + MI -2.46268657 k Units m/sA 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?