The coordinates of a particle moving in the XY plane are given as function of time by: X = 5m + ( 7 m/s^4) t^4 Y = ( 10 m/s)t + (3 m/s^5)t^5  a. Find the position vector of the body at t = 3.5 sec b. Find the instantaneous acceleration of the body at t = 3.5 sec  c. Find the average velocity during the time interval from t 1 = 2 sec to t2 = 4.5 sec

Dock diving is great form of athletic competition for dogs of all shapes and sizes. Sheba, the American Pit Bull Terrier, runs and jumps off the dock with an initial speed of 9.02 m/s at an angle of 25.0° with respect to the surface of the water. Sheba begins at a height of 0.840 m above the surface of the water. What is her total time of flight up until the instant before she hits the water? Express your answer in seconds.

A particle has a position in space given by r = 2t^3 i + 4t^2 j - 3t k where r is in m and t in seconds. Find the magnitude of the instantaneous velocity at t = 3.0 s. 24 m/s 75 m/s 54 m/s 59 m/s

Suppose the position vector for a particle is given as a function of time by r(t) = x(t)î + y(t)j, with x(t) = at + b and y(t) = ct + d, where a = 2.00 m/s, b = 1.15 m, c = 0.116 m/s2, and d = 1.08 m. (a) Calculate the average velocity during the time interval from t = 2.25 s to t= 3.80 s. m/s (b) Determine the velocity at t = 2.25 s. v = m/s Determine the speed at t = 2.25 s. m/s

A particle confined to the xy-plane is in uniform circular motion around the origin. The x- and y-coordinates of the particle vary with time as follows: x(t) = r sin(cot) y(t) = r cos(cot). where >= 2.60 m and c = 2.15 s-¹. What are the x- and y-components of the particle's acceleration at an instant when x = 1.00 m and y = 2.40 m. Give your answers by entering numbers into the empty boxes below. ax || || X x² ms ms-2.

A particle moves in a circular path at constant speed. The initial location of the particle is (4.24 m, 6.05 m) at t = 4 s. The velocity of the particle at this time is 3.02 m/s 3 (i.e., directed along the positive y-axis). Acceleration at this time is along the +x axis. At t=10.6 s, v is -3.02 m/s i and the acceleration is directed along the +y axis. Find the radius of the circle. For this problem assume the time interval is less than one full period. T Find the x-coordinate of the center of the circle (in meters): Xcenter m = m Question Help: Read

Find the velocity and position vectors of a particle that has the given acceleration and the given initial velocity and position. a(t) = eti + sin2tj + cos3k, v(0) = i r(0) = j

Please answer parts a through c