Question

Find the velocity and acceleration of a particle which moves along the curve X=2sin3t, Y=2cos3t and Z=8t at any time t>0. Find the magnitude of the velocity and acceleration

Answer 1

PLS MARK ME BRAINLIEST

Given: Question Details Find the velocity and acceleration of a particle which moves along the curve x=2sin3t, y=2cos3t, z=8t at any time t>0. Find the magnitude of the velocity and acceleration.

SOLUTION:

We have the derivatives of the x , y , and z components with respect to time are :

dx/dt = 6cos3t ,

dy/dt = -6sin3t ,

dz/dt = 8 .

The magnitude of the velocity is ;

|v| = sqrt[ 6^2(cos^2t+sin^2t)+8^2]

= sqrt[36(1)+64]

= sqrt(100)

= 10 ----------- solution

The second derivatives of the components are :

d^2x/dt^2 =

-18sin3t ,

d^2y/dt^2 = -18cos3t ,

d^2z/dt^2 =0

The magnitude of the acceleration is :

|a| = sqrt((-18)^2(sin^2(3t) + cos^2(3t)))

= sqrt[(18)^2(1)]

= 18 --------- solution .