Suppose the position vector for a particle is given as a function of time by r (t) = x(t)i + y(t)j, with x(t) = at + b and y(t) = ct2 + d, where a = 1.70 m/s, b = 1.45 m, c = 0.135 m/s2, and d = 1.04 m. (a) Calculate the average velocity during the time interval from t = 1.95 s to t = 4.05 s. V = 1.71 + 0.0182j m/s X (b) Determine the velocity at t = 1.95 s. 2.4431 + 0.5515j m/s X Determine the speed at t = 1.95 s. 2.9951 X Your response differs from the correct answer by more than 10%. Double check your calculations. m/sThe coordinates of an object moving in the xy plane vary with time according to the equations x = -5.32 sin cut and y = 4.00 - 5.32 cos cut, where w is a constant, x and y are in meters, and t is in seconds. (a) Determine the components of velocity of the object at t = 0. (Use the following as necessary: (.) m/s (b) Determine the components of the acceleration of the object at t = 0. (Use the following as necessary: (.) a = m/s2 (c) Write expressions for the position vector, the velocity vector, and the acceleration vector of the object at any time t > 0. (Use the following as necessary: omega for w and t.) m V = m/s a = m/s2 (d) Describe the path of the object in an xy plot.A particle initially located at the origin has an acceleration of a - 1.00j m/s2 and an initial velocity of vi = 9.001 m/s. (a) Find the vector position of the particle at any time t (where t is measured in seconds). tit (2 j ) m (b) Find the velocity of the particle at any time t. t j) m/s (c) Find the coordinates of the particle at t - 3.00 s. X = m y m (d) Find the speed of the particle at t = 3.00 s. m/s\fA fish swimming in a horizontal plane has velocity v; = (4.00 1 + 1.00 j) m/s at a point in the ocean where the position relative to a certain rock is ri = (16.0 1 - 1.60 j) m. After the fish swims with constant acceleration for 15.0 s, its velocity is v = (15.0 i - 6.00 j) m/s. (a) What are the components of the acceleration of the fish? ax = m/s2 av m/s2 (b) What is the direction of its acceleration with respect to unit vector i? counterclockwise from the +x-axis (c) If the fish maintains constant acceleration, where is it at t = 30.0 s? X = m y m In what direction is it moving? counterclockwise from the +x-axis