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Question 2 A particle moves along a curve given by r(t)-et,t2t> from the point(0,0,0) to the...
EX #1: For t > 0, a particle moves along a curve so that its position at time t is (x(t), y(t)), where x(t) = 4t and = 1 - 2t. Find the time t at which the speed of the particle is 5.
et F(r, v) (3z2e* + sec z tan z,ze - 90y*). (a) Show that F is a conservative. (b) Find a function f (potential function) show that F Vf. (c) Use above result to evaluate JeFdr, where C is a smooth curve that begin at the point (2, 1) and ends at (0, 3). (cost, sint) from -2 to t = 줄 particle that moves along the curve. (Write the value of work done without evaluating d) Find the work...
all questions clearly solved please (2) If the point of application of a force F: R3 R moves along a curve C, then the work done by the force is W F.dr. (a) Find the total work done on an object that traverses the curve c(t) (cos(t), 2 sin(t), (b) Find the total work done on an object that traverses the straight line from (1,0,-2) (c) Explain why the answers in the previous two questions coincide and provide a way...
A particle moves along the x-axis with velocity given by v(t) = 32 – 1 for time t > 0. If the particle is at position x = 5 at time t = 0, what is the position of the particle at timet 1?
3. The particle moves along a planar curve y = et, where r and y are measured in meters. It has a constant speed v = 12 m/s. Then the tangential and normal components of acceleration are at = m/s2 and an = m/s2 at y= 1 m. (Express the answer to two significant p=(1+roji figures. Hint: ) = (TT51FTS) 13: 23:
Consider a particle moving in the plane along the curve r(t) = (R cos(wt), R sin(wt)), where tER, for some constants Row >0. (i) (_marks:) Determine the distance the particle travels for t € [T, 47]. (ii) marks) Suppose the plane has a voltage given by V(x, y) = xy +3. Determine the rate of change in voltage the particle experiences at time t.
A particle moves from the origin to the point x = 3.0 m , y = 27 m along the curve y=ax2−bx, where a = 4.0 m−1 and b = 3.0. It is subject to a force F⃗ =cxyı^+dȷ^, where c = 9.0 N/m2 and d = 19 N . Calculate the work done by the force.
A point particle with mass M moves along a straight line under the influence of a net force that is a function of time, given by: Fx=Bt2, where B is positive and constant. a) If the particle starts from rest, find how long it will take it to cover a distance L. b) Find the speed of the particle after it has traveled a distance L. c) Find the work done on the particle by the net force over the...
3r2, 2ye on a particle that moves once along the parabola y2 +6 from (6,0) to (7,1). (1 point) Find the work done by the force field F(, y) = The curve can be parametrized by r(t) = Σ Σ Σ t e (use the most natural parametrization) Express the line integral in terms of t Σ dt. Work= where Σ Σ Evaluate the integral Σ Work
Prob. 3 If a 2-kg particle moves along a path given by: r(t) = 5 m = constant, and (35) e(t) = 2t rads with t in seconds (36) Sketch and name the entire motion path, and determine the magnitude of the net force and acceleration at any time that you choose.