182k views
4 votes
R(t) is the position of a particle in the xy-plane at time t. 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 the given value of t.

r(t) = (cos 2t)i + (3sin 2t)j; t = 0

User Zareen
by
8.8k points

1 Answer

5 votes

Final answer:

The equation in x and y for the path of the particle is x = cos(2t) and y = 3sin(2t). The velocity vector is v(t) = -2sin(2t)i + 6cos(2t)j. The acceleration vector is a(t) = -4cos(2t)i - 12sin(2t)j.

Step-by-step explanation:

The equation in x and y for the path of the particle can be found by replacing t in the given position vector r(t) = (cos 2t)i + (3sin 2t)j with x and y.

Therefore, the equation in x and y is:

x = cos(2t)

y = 3sin(2t)

To find the velocity vector, we differentiate the position vector with respect to t:

v(t) = -2sin(2t)i + 6cos(2t)j

At t = 0, the velocity vector is:

v(0) = -2sin(0)i + 6cos(0)j = 0i + 6j = 6j

To find the acceleration vector, we differentiate the velocity vector with respect to t:

a(t) = -4cos(2t)i - 12sin(2t)j

At t = 0, the acceleration vector is:

a(0) = -4cos(0)i - 12sin(0)j = -4i

User Turnerj
by
8.2k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories