Thread: Displacement of a particle

Ok I'm guessing this is simple harmonic motion?
I don't understand how these values relate to the displacement at all, can anyone help?


The displacement, d, in cm, of a particle is given by
d = 3 sin(40 π t) – 4 cos( 40 π t ) t ≥ 0
· Find expressions for the velocity and acceleration of the particle
· Calculate the velocity and acceleration when t = 2
· Determine when the particle is first at rest
· Calculate the displacement and acceleration when the particle is at rest

(π = pi)


Thanks!

Find the derivative to get the velocity, and the second derivative to find the acceleration with respect to time.

Are you sure?

Originally Posted by srh

Are you sure?

Yes.

Motion graphs and derivatives - Wikipedia, the free encyclopedia

Then when is the particle at rest?

Particle at rest when velocity =0.









and then solve for t....

Thanks for your time but that doesn't help me in the slightest I'm afraid.

Can this be explained in a more simplistic way?

Also the π symbol is supposed to be the pi symbol

Originally Posted by srh

Also the π symbol is supposed to be the pi symbol

Use the reply with quote tab. On the tool bar you see that is the LaTeX rap.
[TEX]\pi [/TEX] gives .

The displacement, d, in cm, of a particle is given by
d = 3 sin(40 π t) – 4 cos( 40 π t ) t ≥ 0
· Find expressions for the velocity and acceleration of the particle

So we know how to get velocity and acceleration i.e.

--> which is the derivative of displacement
--> which is the derivative of the velocity.

Calculate the velocity and acceleration when t = 2

now we substitute t=2 into the above:




Say the part you don't understand

Any of it really :S

Originally Posted by srh

Thanks for your time but that doesn't help me in the slightest I'm afraid.

Can this be explained in a more simplistic way?

For this problem to make any sense to you at all, you have to know some Calculus. Are you taking a Calculus course? If not, what course is this for?

I'm studying mechanical engineering, I've got only a basic grasp of calculus from what I've been able to teach myself online.

These are equations that describe the motion.

Let's take a simple example

displacement = t for

For the 1st second: displacement = 1 cm
For the 2nd second: displacement = 2 cm and so on....

One can easily that the velocity is 1cm per second.
So how do we do this mathematically,
we use the formula = derivative of displacement
from now on I will use s to refer to displacement...

velocity = (t)= 1 cm per second.

Now to calculate the acceleration:
You the same as above but now you take the derivative of the velocity, so we get

acceleration = (1)= 0.

You can verify this by seeing that the velocity is constant.

Second example

for

For the 1st second: displacement = 1 cm
For the 2nd second: displacement = 4 cm and so on....

we use the formula = derivative of displacement
from now on I will use s to refer to displacement...

velocity = = 2t cm per second.

so if t=1, v= 2(1) = 2; if t=2, v= 2(2) = 4

Now to calculate the acceleration:

acceleration = (2t)= 2cm per second squared.

Now apply the same principles to your equations...