Find the derivative to get the velocity, and the second derivative to find the acceleration with respect to time.
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!
So we know how to get velocity and acceleration i.e.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
--> which is the derivative of displacement
--> which is the derivative of the velocity.
now we substitute t=2 into the above:Calculate the velocity and acceleration when t = 2
Say the part you don't understand
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...