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- find the derivitive, r'(t), of the vector function. r(t)=a+3tb+t^7cHow do you find the velocity and acceleration vectors at t=-1?The position of a particle in the xy-plane at timet is r(t) = (t+ 1) i+ (t - 3) j. Find an equation in x and y whose graph is the path of the particle. Then find the particle's velocity and acceleration vectors at t = 5.
- The position vector r describes the path of an object moving in space. Position Vector Time r(t) = t²i + tj + 4t³/2k t = 4 (a) Find the velocity vector v(t), speed s(t), and acceleration vector a(t) of the object. v(t): = s(t) = a(t) = (b) Evaluate the velocity vector and acceleration vector of the object at the given value of t. v(4) = a(4): =Find the maximum rate of change of f at the given point and the direction in which it occurs. f(x, y) =8xy2, (5,-7) maximum rate of change direction vectorFind the direction in which the maximum rate of change occurs for the function f(x, y) 5x sin(xy) at the point (2,3). Give your answer as a unit vector.
- Q3. For the motion vector r(t) = ti+ In (cost) j, find (i) The velocity (ii) The speed at t=7T (iii) Write the form of acceleration in a(t) = a- T + aN N قمت بالإجابة على السوال الثالثThe position vector r describes the path of an object moving in space. Position Vector Time r(t) 3ti + tj + 1 t²k t = 4 8 (a) Find the velocity vector v(t), speed s(t), and acceleration vector a(t) of the object. =The position of a particle in the xy-plane at time t is r(t) = (t + 4) i+(²+2) j. Find an equation in x and y whose graph is the path of the particle. Then find the particle's velocity and acceleration vectors at t=4. The equation for the path of the particle is y=