Question

Guys need help to get the answer for the below qn? please help....

A particle is moving along the curve given by the equation r(t) = 2t i + t^2 j +lnt k

a) find velocity of the particle

b) the speed

c) distance travelled from t=0

d) acceleration

e) tangential acceleration

f) the acceleration normal to the tangent and

g) the radius of curvature


any hope????

Answer 1

velocity is \(r'(t)\)
speed = \(|r'(t)|\)
distance traveled =\(\displaystyle \int_0^{t} |r'(s)|\mathrm ds\)

Answer 2

hope for the best :) ...welcome to openstduy !

Answer 3

acceleration is \(r''(t)\)

Answer 4

tangential acceleration = \(\displaystyle \frac{r''(t)\cdot r'(t)}{|r'(t)|^2}r'(t)\)

Answer 5

acceleration normal = acceleration - tangential acceleration

Answer 6

radius of curvature \(\rho(t)\)
\[\Large\rho(t)=\frac{|r'(t)|^3}{|r'(t)\times r''(t)|}\]

have fun. =)

Answer 7

great thanks