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

[Indranil]

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

 

[lekh2003]

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).

 

[Indranil]

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?

 

[lekh2003]

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.

 

[CWatters]

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?

 

[Indranil]

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

 

[Indranil]

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

 

[Mark44]

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

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.

 

[CWatters]

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.

 

[lekh2003]

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.