S = 12t and S = 490t^2 What do they mean?

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In summary: S/t)^0.0008812 = (12/5)^0.00088For 2...S = 490t^2so490 = S*t^2S is in meters and t...t is in seconds so490 = (S*t^2)^0.000488490 = (490/25)^0.000488In summary, the equations state that the displacement of an object changes by 12 meters and 490 seconds after a certain amount of time has elapsed.
  • #1
Indranil
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1. The problem statement, all variables, and given/known data
1. S = 12t, where S = displacement ant t = time (in seconds)
2. S = 490t^2, where S = displacement and t = time (in seconds)
What do the two equations mean here? I don't understand what they want to mean here. I am confused.
Could you draw the graphs in support of the two equations above?

Homework Equations


1. S = 12t, where S = displacement ant t = time (in seconds)
2. S = 490t^2 where S = displacement and t = time (in seconds)

The Attempt at a Solution


What I only know here S = displacement and t = time in seconds
 
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  • #2
Think about the equations in terms of x and y (S being x and t being y). Then think about the common forms you are aware of ( y = mx +b, y=ax^2). I think they want you to try to verbally explain the equations. As this happens, this happens. You can easily draw the graphs using existing graphing knowledge which I assume you have.

You can check if you have the graphs right by putting the equations into a graphing calculator (desmos probably).
 
  • #3
lekh2003 said:
Think about the equations in terms of x and y (S being x and t being y). Then think about the common forms you are aware of ( y = mx +b, y=ax^2). I think they want you to try to verbally explain the equations. As this happens, this happens. You can easily draw the graphs using existing graphing knowledge which I assume you have.

You can check if you have the graphs right by putting the equations into a graphing calculator (desmos probably).
Still, I don't understand what you mean. Could you make your point easier, please?
 
  • #4
Indranil said:
Still, I don't understand what you mean. Could you make your point easier, please?
It would help if you could give me some context. Are you studying this for physics? math? graphing?

I can help you accordingly, since I would understand what the question wants you to answer.
 
  • #5
Indranil said:
1. The problem statement, all variables, and given/known data
1. S = 12t, where S = displacement ant t = time (in seconds)
2. S = 490t^2, where S = displacement and t = time (in seconds)
What do the two equations mean here? I don't understand what they want to mean here. I am confused.
Could you draw the graphs in support of the two equations above?

Do a unit (dimensional) analysis...

For 1.: If t is in seconds and S is in meters what must the units associated with the 12 be?

For 2.: likewise if t is in seconds and S is in meters what are the units associated with the 490?
 
  • #6
lekh2003 said:
It would help if you could give me some context. Are you studying this for physics? math? graphing?

I can help you accordingly, since I would understand what the question wants you to answer.
Sir, I am studying this for physics and math
 
  • #7
CWatters said:
Do a unit (dimensional) analysis...

For 1.: If t is in seconds and S is in meters what must the units associated with the 12 be?

For 2.: likewise if t is in seconds and S is in meters what are the units associated with the 490?
For 1. It would be 12 seconds and for 2. it would 490 seconds^2
If I am wrong here please correct me
 
  • #8
Indranil said:
1. The problem statement, all variables, and given/known data
1. S = 12t, where S = displacement ant t = time (in seconds)
2. S = 490t^2, where S = displacement and t = time (in seconds)
What do the two equations mean here? I don't understand what they want to mean here. I am confused.
Could you draw the graphs in support of the two equations above?

Homework Equations


1. S = 12t, where S = displacement ant t = time (in seconds)
2. S = 490t^2 where S = displacement and t = time (in seconds)

The Attempt at a Solution


What I only know here S = displacement and t = time in seconds
Indranil said:
Sir, I am studying this for physics and math
Since you're studying physics as well as math, the equations model a physical situation where something is moving.

In equation 1, each second that elapses, the displacement s changes by 12 units. What sort of motion is implied here? IOW, is the object accelerating, decelerating, or moving at constant speed?

In equation 2, what is the displacement at t = 0 seconds? At t = 1 second? At t = 2 seconds? Is the object acclerating, decelerating, moving at constant speed, not moving at all?

Since you are also studying math, it might be helpful to sketch the graphs of these two equations, with the t-axis horizontal and the s-axis vertical.
 
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  • #9
Indranil said:
For 1. It would be 12 seconds and for 2. it would 490 seconds^2
If I am wrong here please correct me

No that's not correct.

For 1...

S = 12t
so
12 = S/t

S is in meters and t in seconds so the 12 is actually 12 m/s (meters per second) which makes it a velocity.

In other words eqn 1 is of the form

Displacement = Velocity * time

Can you try something similar for 2.
 
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  • #10
Indranil said:
Sir, I am studying this for physics and math

I think you just have to describe the movement of the object following the path defined by the equation. "As the object displaces by S, time will progress proportionately". Try and think of a description of the particle. Draw a time VS displacement graph and try and follow the particle. Try and visualize.

P.S. No need to call me Sir, I am in high school.
 

FAQ: S = 12t and S = 490t^2 What do they mean?

What is the meaning of the equation S = 12t?

The equation S = 12t represents a relationship between distance (S) and time (t). Specifically, it means that the distance traveled (S) is equal to 12 times the time (t).

How is the equation S = 490t^2 interpreted?

The equation S = 490t^2 also represents a relationship between distance and time, but in this case, the distance traveled (S) is equal to 490 times the square of the time (t). This means that as time increases, the distance traveled increases at a much faster rate.

What do the variables S and t stand for in these equations?

In both equations, S represents the distance traveled and t represents the time elapsed. These variables are used to quantify the relationship between distance and time.

Are these equations used for a specific scientific concept or application?

Yes, these equations are commonly used in physics to analyze the motion of an object. They are often used to calculate the distance an object travels over a certain period of time or to determine the speed of an object.

Can these equations be used for any type of motion or only for linear motion?

The equation S = 12t can be used for any type of motion, as long as the object is moving at a constant speed. However, the equation S = 490t^2 is specifically used for objects undergoing constant acceleration, such as free-falling objects or objects moving in a curved path.

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