Acceleration & Velocity v Time: Is a Sine Curve Possible?

In summary, the force and acceleration v time graphs would have the same shape if the force v time graph is a sine curve. This is because acceleration is the derivative of velocity, which is the derivative of position. Therefore, the acceleration v time graph would also be a sine curve. However, the velocity v time graph would be shifted to the right by pi/2. The magnitude of a force is never negative in classical physics, but the minus sign in front of the cosine in the integration from acceleration to velocity has to do with orientation along some given axis. The time dependent curves for force and acceleration are the same because F=ma and the only difference is the constant mass. The force v acceleration graph would be a straight line through the
  • #1
UrbanXrisis
1,196
1
If a force v time graph made a sine curve, then the acceleration v time would create a sine curve too correct? However, the velocity v time curve would look like a pi/2 shift to the right? Are these thoughts correct?
 
Physics news on Phys.org
  • #2
yes going from acceleration to velocity can be done by integrating the sine. This yields a cosine (with minus sign in front of it) and as you know sin(x) = cos(90°-x)...

marlon
 
  • #3
when is force negative?

And why is force v time and acceleration v time the same curve?
 
  • #4
when the force vector points in the opposite direction of the x-axis for example.

The magnitude of a force is never negative in classical physics...
The minus sign has to do with orientation along some give axis.

marlon
 
  • #5
The time dependent curve is the same for force and acceleration because F=ma. So basically the only difference is the mass, which is constant during the entire motion.

marlon
 
  • #6
I'm starting to understand, but I'm still a little iffy on the negative force. Say a cart moves towards the origin slowing down and at a steady rate, it turns around after 2 seconds and then moves away from the origin speeding up at the same steady rate. The v vs t graph would look like a steady positive slope from negative to positive where x=0 at 2 seconds...what would force look like?
 
  • #7
when the acceleration vector is positive, it means you go faster and faster. When it is negative you are slowing down. Same thing for the force-vector since it is the acceleration vector multiplied by a positive constant (the mass)

marlon
 
  • #8
ohhh, so the force vs time is the same as the acceleration vs time graph?! because mass is always constant!
 
  • #9
yes it is...
marlon
 
  • #10
what about a force vs acceleration graph? It would just be a straight line?
 
  • #11
well yes if a is one definite value.
You can also plot the force v a for different a values, then you would get a straight line through the origin.

marlon
 
  • #12
when two equal forces are applied to an object...one form the left and the other from the right...the object is kept stationary, however, the new force would be the combination of both forces from the left and right correct?
 

FAQ: Acceleration & Velocity v Time: Is a Sine Curve Possible?

Can acceleration or velocity be represented by a sine curve?

Yes, acceleration and velocity can be represented by a sine curve. This is known as harmonic motion, where the acceleration or velocity of an object is proportional to the displacement from its equilibrium position.

What causes a sine curve in acceleration or velocity?

A sine curve in acceleration or velocity is caused by a restoring force that is proportional to the displacement of the object. This type of motion is commonly seen in systems with springs or pendulums.

Is a sine curve possible for all types of motion?

No, a sine curve is not possible for all types of motion. It is only possible for harmonic motion, where the restoring force is proportional to the displacement.

How can a sine curve be used to analyze motion?

A sine curve can be used to analyze motion by determining the amplitude, frequency, and phase of the curve. These parameters can provide information about the acceleration, velocity, and displacement of the object.

Can a sine curve be used to predict future motion?

Yes, a sine curve can be used to predict future motion as long as the system remains in a state of harmonic motion. By analyzing the parameters of the curve, future positions, velocities, and accelerations of the object can be estimated.

Similar threads

Derivation for modified sine curve equations
Replies
6
Views
1K
Finding the change in velocity from an acceleration vs time graph
Replies
1
Views
3K
Relating acceleration to distance and time
Replies
5
Views
2K
Is it possible to solve relative velocity problems without sine law?
Replies
25
Views
1K
In a constant acceleration motion, Is it possible to have constant speed?
Replies
11
Views
976
Average Vector Acceleration Along a Curve and a Straight Section
Replies
4
Views
1K
Inconsistency in a Velocity-Time Graph
Replies
13
Views
3K
Zero velocity for a time interval, what about acceleration?
Replies
7
Views
1K
Instantaneous Acceleration Given Equation for Velocity
Replies
7
Views
677
Find the change in the time required, if acceleration increases by the differential amount 'da'
Replies
7
Views
583

Hot Threads

Recent Insights

Back
Top