A particle moving along the curve given byr = 3 + 2cos 0 has position (x(t), y(t)) at time t, with 0 = 0 when t = 0. This particle moves along the curve so that Find the at 0 = and specify if the particle is moving towards or away from the pole at this time.

Q: A particle moves along the curve *= 21² , y = t² – 4t and = = 31 – 5 where t is the time . Find the…

A: Given: Position vector is given as, r→=2t2i^+(t2-4t)j^+(3t-5)k^ The objective is to find the…

Q: 4. The function a(t) = 3t² – 20t + 27 describe the acceleration of a particle moving along a line.…

A: Given that: Acceleration function, a(t)=3t2-20t+27

Q: Q2) Use the chain rule to express dy /dx in terms of x and y y = sint and t = cos x where t= 0

A:

Q: Find the length of the curve y = In(e - 1) – In(e + 1), In 2 sxsIn 3.

A:

Q: A particle is moving with the given data. Find the position of the particle. a(t)= t^2 -5t + 4,…

A:

Q: Let 7 (t) = (2 – 5t2)i – (9t°)j – 4tk be the position of particle in space at time t. The %3D speed…

A: The speed of the particle at t=0 is 4

Q: Consider a particle moving along a curve so that it is at position f(t) = (2t³, 2+²) at time t. Then…

A: Given, A particle is moving along a curve such that its position is at ft=2t3,2t2 at time t.

Q: Let y(1) = (1/2)teit/2. 0 <t< 2n What is the terminal point of the curve? IT —2л

A:

Q: Compute r"(t) and r'''(t) for the following function. r(t) = (7t2 + 4,t + 3,6)

A:

Q: 2. A particle starting with velocity u is falling freely under gravity with a constant acceleration.…

A: Introduction :

Q: find dy/dx if y=((t-1)/(t+1))^2 and x= (1/t^2)-1 at t=2

A:

Q: Find the value of the derivative dy/dx at  t=2π/3 when an object moves according to the parametric…

A:

Q: Jack drives east away from Hilltop bakery at 60 mph while Jill drives toward the bakery at 40 mph…

A: Given that,

Q: Find T, N and B for the curve 7(t) (2 cos(2t), 2 sin(2t), 5t) at the point t = 0 Give your answers…

A:

Q: 6. Find where the velocity of a particle is zero if its position function is x(t)= t In t

A:

Q: C is the curve y = e® from (2, e²) to (0,1) and F = (x², -y), compute ſ, F-dr.

A: Given that, C is the curve y=ex from 2,e2 to 0,1 and F=x2,-y Then, F=x2,-y=x2,-ex So, F→=x2i^-exj^

Q: Q3) for f(t) = sec-(6t- 1) and g(t) = tan (6t - 1) show that s'() = g'(t). %3D

A: