Find the velocity, acceleration, and speed of a particle with the given position function. r(t) = (4 cos(t), 6t, 4 sin(t)) %3D v(t) (-4 sin (t),6,4 cos(t)) %3D a(t) (-4 cos(1),0, – 4 sin (1)) %3D |v(t)| II

Q: x= 4 sin t - 4, y = 4 cos t -3 Eliminate the parameter t

A: we can eliminate 't' . sin2 t + cos2t =1

Q: What is the particle's starting position (t = 0);

A: We have to find

Q: Solve the Linear 1st Order O.D.Es:

A: Given that the differential equation is

Q: A particle is moving with the given data. Find the position of the particle. v(t) = sin(t) – cos(t),…

A: Given that  v(t)=sin(t)-cos(t) and s(0)=3. We have to find s(t).

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.