6) A particle moves according to r(t)=<1,t,t^2)> where x(t),y(t) and z(t) are all given in meters and t in seconds. a) How fast and in what direction (give direction as a unit vector) is the particle traveling in at time t=1? b) Find the curvature when t=1. c) Find the unit normal when t=1 d) Find an equation for the Osculating plane (determined by T and N) when t = 1.
6) A particle moves according to r(t)=<1,t,t^2)> where x(t),y(t) and z(t) are all given in meters and t in seconds. a) How fast and in what direction (give direction as a unit vector) is the par...
A 0.200 kg particle moves along an x axis according to particle at t-3.30s?Give an expression for the (a) x, (b) y and (c) z components. 140 + 2 O t + 2.00 t2 400 t3 with x in meters and tin seconds ln unit-vector notation, what is the net force acting on the (a) Number Units (b) Number Units (c) Number Units
(1 point) A stone is thrown from a rooftop at time t 0 seconds. Its position at time t (the components are measured in meters) is given by r()-бі-50+ (24.5-49:2) k. The origin is at the base of the bulding, which is standing on flat ground. Distance is measured in meters. The vector i points east,j points north, and k points up. (a) How high is the rooftop? meters. (b) When does the stone hit the ground? seconds (c) Where...
The position vector of a point which moves in the x-y plane is given by: r = (- 0.2 t4 + 1.8 t3 + 1.1 t2) i + (- 0.4 t4 - 1.2 t) j where r is in meters and t is in seconds. Determine the angle between the velocity v and the acceleration a when t = 1.7 sec.
A particle moves and its vector is given by ? = ??? + (? − ??)? find (a) a unit vector normal to the trajectory at t =1 (b) The angular momentum ? = ? × ??̇ of the particle where ?̇ = ?r/?t (c) The torque ? = ? × ??̈ on the particle where ?̈= ???/??2 Note: from (b) and (c) it is easily seen that ? = ?l/?t Please show all workings out and thanks for your...
A particle moves along the x axis according to the equation X(t) = 2 + 3t + 4t 2, where x is in meters and t is in seconds. What is the instantaneous acceleration at t = 3s A) 1.0 m/s? B) 3.0m/s? C) 4.0 m/s? D) 8.0 m/s? OOOO
A detailed explanation would be highly appreciated Question 2 25 (2.1) Consider the vector function C defined by r(t)-ti+2 j. (a) Find the unit tangent, the unit normal and binormal veetors T(t). N(t) and B(t) for C. (6) (b) Find an equation for the normal plane of C at the point (1, 2) (3) (c) Find an equation for the osculating cirele of Gat the turning point of C. (4) (2.2) Reparametrize the curve r(t) (e ,V2t , e) with...
The vector position of a particle varies in time according to the expression r = 8.20 i-5.60p j where r is in meters and t is in seconds. (a) Find an expression for the velocity of the particle as a function of time. (Use any variable or symbol stated above as necessary.) x m/s Determine the acceleration of the particle as a function of time. (Use any variable or symbol stated above as necessary.) X m/s2 (c) Calculate the particle's...
The velocity vector of an object is given by y(t) = (* sin(at), 1, a cos(at)). Assume that at t = 1, the object is at the point P(1,1,0). (a) Find the position vector F(t) of the object. (b) Find parametric equations of the line which is tangent to r(t) at P. (c) Find the distance that the object traveled from the point t = 0 to t = 1. (d) Find an equation for the normal plane of r(t)...
A particle moves with position given by s(t) = t 1 with t > 0. + where s is in meters and t is in seconds (a) Find the velocity function u(t). (b) Find v(2). Include units in your answer. (c) Find the acceleration function a(t). (d) When is the particle at rest? (You only need to consider t 0.) (e) Find the total distance traveled by the particle on 0 STS 3.
(1 point) A body of mass 10 kg moves in the xy-plane in a counterclockwise circular path of radius 3 meters centered at the origin, making one revolution every 11 seconds. At the time t 0, the body is at the rightmost point of the circle. A. Compute the centripetal force acting on the body at time t. B. Compute the magnitude of that force. HINT. Start with finding the angular velocity o [rad/s] of the body (the rate of...