All following questions refer to a particle whose trajectory in time is given by

Question

All following questions refer to a particle whose trajectory in time is given by the vector function. r(t)=. 1. What is the velocity of the particle at time t=0? 2. What is the speed of the particle at t = 0 ? 3. Is the speed of this particle constant? 4. Find the arc length function s(t) of the helix r(t) with s(0) = 0 for t>=0 and reparameterize the helix with respect to this arc length. 5. What is the acceleration vector of the particle at t = 0? 6. Find the unit tangent vector T and unit normal vector N at t= 0. 7. Find the tangential and normal components of the acceleration (aT and aN) at t=0. 8. Compute the curvature ?? of the helix r(t).

Explanation / Answer

dude actually the figures are not clear in the question so i can't tell you the correct answer but i'm providing you the theory required to crack them: if r(t) is given then 1)v(t) = dr(t)/dt 2)speed=distance/time and distance you can find out with the help of r(t) 3)that depends upon r(t). 4)r(t) can be divided into its x and y component i.e. X(t) and y(t) hence arc length=sqrt([x'(t)]^2 + [y'(t)^2]) 5)a=dv(t)/dt

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.