Velocity and accleration of a particle

[nick227]

Homework Statement

A particle moves along a curve whose equations are:
x=3e^(-2t)
y=4sin3t
z=5cos3t
where t is the time.
a) Find the velocity and acceleration at any time.
b) Find the magnitudes of the velocity and acceleration at time t=0.

Homework Equations

The Attempt at a Solution

I know that the velocity is d/dt of the position and acceleration is d/dt of velocity. How can i find the velocity? If i take the derivative of all three functions, i will get three different velocities.

 

[Dick]

How is the magnitude of a vector related to it's components?

 

[nick227]

How is the magnitude of a vector related to it's components?

the magnitude is the square root of the components squared.

 

[Dick]

Right! So apply that to the velocity and acceleration vectors to get the magnitude.The three different velocities and accelerations are components of vectors.

 

[nick227]

Right! So apply that to the velocity and acceleration vectors to get the magnitude.The three different velocities and accelerations are components of vectors.

so i find the velocities. then i have three different velocities, but i can't find the magnitude if i don't find velocity for a certain t.
v(x)= -6e^(-2t)
v(y)= 12cos3t
v(z)=-15sin3t

a(x)=12e^(-2t)
a(y)=-36sin3t
a(z)=-45cos3t

now what...?

 

[Dick]

Ordinarily, I would just say find the magnitudes as a function of t. But your problem says find them at t=0.

 

[nick227]

Ordinarily, I would just say find the magnitudes as a function of t. But your problem says find them at t=0.

well i can do part b with t=0. what about part a? i mean i have three different velocities and three different accelerations. for velocity, if i take the three components and square them then add them and find the square root, that gives the speed. its not a velocity at any time t. I'm assuming for part a, i need just one equation for velocity and one for acceleration.

 

[Dick]

so i find the velocities. then i have three different velocities, but i can't find the magnitude if i don't find velocity for a certain t.
v(x)= -6e^(-2t)
v(y)= 12cos3t
v(z)=-15sin3t

a(x)=12e^(-2t)
a(y)=-36sin3t
a(z)=-45cos3t

now what...?

Your vector v above is the velocity at any time t. If you want a specific time then plug it in but if they say for ANY t, then that's the answer. Ditto for a.

 

[nick227]

Your vector v above is the velocity at any time t. If you want a specific time then plug it in but if they say for ANY t, then that's the answer. Ditto for a.

aren't there three vectors? three different equations for v? don't they want only one equation for velocity? and one for acceleration?

 

[Dick]

No, there is one vector v(t)=(-6e^(-2t),12*cos(3t),-15sin(3t)). The vector has three components. You are done.

 

[nick227]

No, there is one vector v(t)=(-6e^(-2t),12*cos(3t),-15sin(3t)). The vector has three components. You are done.

Oh! Well i am done with this problem. Thanks for all the help, much appreciated.