A particle moves along a circular path in such a way that is x- and y- coordinates at time t are x-2cost y-2sin e (i) Find the instantaneous velocity and speed of the particle at time t. (ii) Sketch the path of the particle, and show the position and velocity vectors at time with the velocity vector drawn so that its initial point is at the tip of the position vector. (ii) Show that at each instant the acceleration vector is perpendicular to the velocity vector.

A particle moves along a circular path in such a way that is x- and y- coordinates at time t are x-2cost y-2sin e (i) Find the instantaneous velocity and speed of the particle at time t. (ii) Sketch the path of the particle, and show the position and velocity vectors at time with the velocity vector drawn so that its initial point is at the tip of the position vector. (ii) Show that at each instant the acceleration vector is perpendicular to the velocity vector.

Algebra and Trigonometry (6th Edition)

6th Edition

ISBN:9780134463216

Author:Robert F. Blitzer

Publisher:Robert F. Blitzer

ChapterP: Prerequisites: Fundamental Concepts Of Algebra

Section: Chapter Questions

Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...

See similar textbooks

Related questions

Q: Find the position vector for a particle with acceleration, initial velocity, and initial position…

A: As per given by the question, there are given: a→t=6t, 5sint, cos6tv→0=4, 3, 5r→0=3, -4, -4 Now, For…

Q: Q3: A particle traveling in a straight line is located at the point (1,-1,2) and has speed 2 at time…

A: Solution :-

Q: The position vector r of a moving particle at time t after the start of the motion is given by r…

A: The position vector r of a moving particle at time t after the start of the motion is given by r…

Q: A point moves along a right-circular helix C, which is the curve of the path 7 :R → R³ given by,…

Q: The position vector r describes the path of an object moving in the xy-plane. Position Vector Point…

Q: A sodium ion (Na+) moves in the xy-plane with a speed of 2.90 ✕ 103 m/s. If a constant magnetic…

Q: Sketch the direction field of the DE y'=2x+y. (Plot 9 or more points) Then sketch approximate…

Q: 42. Two boats B, and B2 are moving with velocities (4i – 3j + 7k) ms' and (2i + 3j + 4k) ms…

A: Velocities (4i-3j+7k) and (2i+3j+4k)

Q: Consider the function f(x.y) = x(/y +x) and the point P (3,9). (a) Find the gradident vector of f at…

A: The function f(x,y)=xy+x and the point P=3,9. We have to answer the following...

Q: (b) The path of a moving body is defined by r(t) = costi+ sint j + (2 - sint)k. (i) Show that the…

A: The path of the moving body is given by rt=cos t i+sin t j+2-sintk. The given cylinder is x2+y2=1…

Q: Find the position vector for a particle with acceleration, initial velocity, and initial position…

Q: find the acceleration of a particle whose position function is x(t)=sin(2t)+cos(t)

Q: A point moving a long a curve whose position vector is R(t)=(t sin t +cost)i+(sin t-t cost)j+4 k;…

Q: 9.) A particle moves in a straight line according to the law of motion: s=cos(x). a. Find the…

Q: Suppose that the vector-valued function F(t) = < 3t, cos(5t), sin(5t) represents the position of an…

Q: A particle has initial position vector (4i + 5j) metres. It moves with a constant velocity of (3i –…

A: The given initial position vector is 4i^+5j^ meters. The given velocity is 3i^-2j^ meter per second.…

Q: (c) Suppose the position vector of a moving particle at time t is given by 7(t) = (tv2) î + (e*) j+…

Q: (5) A particle moves in space, its position is specified by the position vector r(1) = (1,r,t sint),…

Question

A particle moves along a circular path in such a way that is x- and y- coordinates at time t are
x= 2cost y-2sin t
(6)
Find the instantaneous velocity and speed of the particle at time 1.
(ii) Sketch the path of the particle, and show the position and velocity vectors at time 1=
with the velocity vector drawn so that its initial point is at the tip of the position vector.
(ii) Show that at each instant the acceleration vector is perpendicular to the velocity vector.

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

This is a popular solution!

SEE SOLUTION Check out a sample Q&A here

Step 1

VIEW

Step 2

VIEW

Step 3

VIEW

Trending now

This is a popular solution!

Step by step

Solved in 3 steps with 3 images

SEE SOLUTION Check out a sample Q&A here

Similar questions

The motion of a point on the circumference of a rolling wheel of radius 4 feet is described by the vector function r(t) = 4(12t - sin(12t))i + 4(1 − cos(12t))j Find the velocity vector of the point. v(t) = Find the acceleration vector of the point. a(t) = Find the speed of the point. s(t) = =
Consider the curve r(t) =(5t² − 3)i + (3t - sin(t))j. - y -5 v(t) = 5 -5 5 10 15 20 (a) Find the velocity of a particle moving along the curve. 25 X (b) Find the acceleration vector of a particle moving along the curve. a(t) =
Q2: A point move in a space with an acceleration vector given by a(t) = 4 sin 2t + 6t j+ e -tk If this point starts in motion from the point (-1, 2, 3) with initial velocity Vo = 2i + 3j – k, find the velocity at any time and the parametric equation of the position motion path
Find the position vector of a particle that has the given acceleration and the specified initial velocity and position. Then on your own using a computer, graph the path of the particle. a(t) = 7ti + e'j + e*k, v(0) = k, r(0) = i+ k r(t) A projectile is fired with an initial speed of 190 m/s and angle of elevation 60°. (Use g = 9.8 m/s?. Round your answers to the nearest whole number.) (a) Find the range (in m) of the projectile. (b) Find the maximum height (in m) reached. m (c) Find the speed (in m/s) at impact. m/s
A particle is moving with velocity V(t) = ( pi cos (pi t), 3t2+ 1) m/s for 0 ≤ t ≤ 10 seconds. Given that the position of the particle at time t = 2s is r(2) = (3, -2), the position vector of the particle at t is?