# Homework Help: Velocity and accleration of a particle

1. Sep 18, 2007

### nick227

1. The problem statement, all variables and given/known data

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.

2. Relevant equations

3. 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.

2. Sep 18, 2007

### Dick

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

3. Sep 18, 2007

### nick227

the magnitude is the square root of the components squared.

4. Sep 18, 2007

### 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.

5. Sep 18, 2007

### nick227

so i find the velocities. then i have three different velocities, but i cant find the magnitude if i dont 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...?

6. Sep 18, 2007

### Dick

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

7. Sep 18, 2007

### nick227

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.

8. Sep 18, 2007

### Dick

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.

9. Sep 18, 2007

### nick227

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

10. Sep 18, 2007

### Dick

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

11. Sep 18, 2007

### nick227

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