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#1 2021-04-11 12:48:24

mathland
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Registered: 2021-03-25
Posts: 438

Rectilinear Motion

As an object in rectilinear motion moves,
its distance s from the origin at time t is given by the equation
s = s(t) = √4t, where s is in centimeters and t is in seconds.
Find the velocity v of the object at t_0 = 1 and t_0 = 4.

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#2 2021-04-11 19:32:01

Bob
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Registered: 2010-06-20
Posts: 9,128

Re: Rectilinear Motion

I know you were advised to split your posts but all the ones you have made are related in that they form an introduction to calculus.  I suggest you get the other (easier) ones sorted first; then we can proceed to the harder ones.

Bob


Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob smile

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#3 2021-04-12 10:30:28

mathland
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Registered: 2021-03-25
Posts: 438

Re: Rectilinear Motion

Bob wrote:

I know you were advised to split your posts but all the ones you have made are related in that they form an introduction to calculus.  I suggest you get the other (easier) ones sorted first; then we can proceed to the harder ones.

Bob

I will take it one at a time. What is rectilinear motion anyway?

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#4 2021-04-12 20:21:51

Bob
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Registered: 2010-06-20
Posts: 9,128

Re: Rectilinear Motion

I've never questioned why it is called that.  Hhmm!  It means an object travelling along a known straight path.  I googled it and was surprised to discover that linear motion means along a path that need not be straight and rectilinear means the path is straight.

In a question, if they give you the equation of motion (eg. s = 5 - t^2) then it doesn't really matter what the path is.

Bob

ps.  This morning I went through all your responses and answered the ones that need an answer at this stage (I hope I didn't miss one).  When I click for active posts my answered ones jump to the top of list and the ones I hadn't looked at yet stayed mixed in with the ones I'm leaving until later. So it's getting harder and harder for me to keep track of whether I've done all I need to.  (hope this is making sense)

So when you are ready to return to an unanswered one from your list, please bump it back to the top by posting that you want me to deal with it.  Hope that makes sense.


Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob smile

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#5 2021-04-14 12:05:16

mathland
Banned
Registered: 2021-03-25
Posts: 438

Re: Rectilinear Motion

Bob wrote:

I've never questioned why it is called that.  Hhmm!  It means an object travelling along a known straight path.  I googled it and was surprised to discover that linear motion means along a path that need not be straight and rectilinear means the path is straight.

In a question, if they give you the equation of motion (eg. s = 5 - t^2) then it doesn't really matter what the path is.

Bob

ps.  This morning I went through all your responses and answered the ones that need an answer at this stage (I hope I didn't miss one).  When I click for active posts my answered ones jump to the top of list and the ones I hadn't looked at yet stayed mixed in with the ones I'm leaving until later. So it's getting harder and harder for me to keep track of whether I've done all I need to.  (hope this is making sense)

So when you are ready to return to an unanswered one from your list, please bump it back to the top by posting that you want me to deal with it.  Hope that makes sense.

Hello. What's new? To respond here, I certainly would appreciate if you fully solve this problem for me. I can then use your reply to answer similar questions. My main problem is not understanding the ideas behind certain topics.

I utilize You Tube lessons, especially by Professor Leonard in my studies.  He is an excellent math teacher. I am taking notes per lesson. Notes given by Professor Leonard are far easier to understand than most math textbooks. What do you think about the Math for Dummies book series?

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#6 2021-04-14 20:25:49

Bob
Administrator
Registered: 2010-06-20
Posts: 9,128

Re: Rectilinear Motion

As an object in rectilinear motion moves,
its distance s from the origin at time t is given by the equation
s = s(t) = √4t, where s is in centimeters and t is in seconds.
Find the velocity v of the object at t_0 = 1 and t_0 = 4.

s is often used in mechanics for distance to avoid confusion with calculus notation, where 'd' has a special meaning.

If you plot the graph of s against t, you'll get a straight line with gradient √4.  The gradient is a measure of velocity as V = D/T so the velocity is √4 at t =1 and t = 4.

It occurs to me that maybe the problem was

You could use limits to get an answer like this:

Let A = (1,2)  Let B = [1.1, √(4.4)]  calculate the gradient of AB using (difference in y coords) / (difference in x coords).

Then recalculate with B = [1.01,√(4.04)].  Continue, gradually moving B closer and closer to A.

Once you have some calculus this question can be answered more easily using differentiation.

Bob


Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob smile

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#7 2021-04-15 14:26:30

mathland
Banned
Registered: 2021-03-25
Posts: 438

Re: Rectilinear Motion

Bob wrote:

As an object in rectilinear motion moves,
its distance s from the origin at time t is given by the equation
s = s(t) = √4t, where s is in centimeters and t is in seconds.
Find the velocity v of the object at t_0 = 1 and t_0 = 4.

s is often used in mechanics for distance to avoid confusion with calculus notation, where 'd' has a special meaning.

If you plot the graph of s against t, you'll get a straight line with gradient √4.  The gradient is a measure of velocity as V = D/T so the velocity is √4 at t =1 and t = 4.

It occurs to me that maybe the problem was

You could use limits to get an answer like this:

Let A = (1,2)  Let B = [1.1, √(4.4)]  calculate the gradient of AB using (difference in y coords) / (difference in x coords).

Then recalculate with B = [1.01,√(4.04)].  Continue, gradually moving B closer and closer to A.

Once you have some calculus this question can be answered more easily using differentiation.

Bob

Thank you. I am familiar with basic differentiation. How can we use differentiation to solve this problem more easily?

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#8 2021-04-15 20:05:42

Bob
Administrator
Registered: 2010-06-20
Posts: 9,128

Re: Rectilinear Motion

If s = √4.t   then ds/dt = √4

If

then

At t = 1, ds/dt = 1

At t = 4, ds/dt = 1/2

Bob


Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob smile

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#9 2021-04-16 07:16:22

mathland
Banned
Registered: 2021-03-25
Posts: 438

Re: Rectilinear Motion

Bob wrote:

If s = √4.t   then ds/dt = √4

If

then

At t = 1, ds/dt = 1

At t = 4, ds/dt = 1/2

Bob

Wonderfully easy. Thanks.

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