How to find the path if we only know the velocity (without common formulas)?

[Mike_bb]

Hello!

I invented the problem and I try to solve it:

Let we only know velocity of moving particle: $v(t)$ from $t=a$ to $t=b$. And we don't know about $F(b)-F(a)$ and other formulas. We can't use formulas directly.

How to find path from $t=a$ to $t=b$? How to reason in this case?
Is this problem can be solved?

Thanks.

 

[PeroK]

Hello!

I invented the problem and I try to solve it:

Let we only know velocity of moving particle: $v(t)$ from $t=a$ to $t=b$. And we don't know about $F(b)-F(a)$ and other formulas. We can't use formulas directly.

How to find path from $t=a$ to $t=b$? How to reason in this case?
Is this problem can be solved?

Thanks.

What's the general relationship between displacement and velocity?

 

[Mike_bb]

What's the general relationship between displacement and velocity?

Neither. We only know $v(t)$.

 

[PeroK]

What is velocity?

 

[Mike_bb]

What is velocity?

Thanks for your hint. I solved my problem!

 

[jedishrfu]

Can you show us what you did?

It helps others following your thread to learn from your work.

Also, we might spot something in your solution that you hadn't considered.

 

[Mike_bb]

Can you show us what you did?

It helps others following your thread to learn from your work.

Also, we might spot something in your solution that you hadn't considered.

The task was: find path of moving particle if only velocity is known. But as I understood it's impossible if we don't know how velocity is calculated (using limit).

 

[jbriggs444]

The task was: find path of moving particle if only velocity is known. But as I understood it's impossible if we don't know how velocity is calculated (using limit).

Impossible? Surely not. In the real world there is a process that has been used for centuries. Dead Reckoning.

In the mathematical world we use a different term.

 

[DaveE]

Have you studied calculus in school yet? How much?

 

[Mike_bb]

Have you studied calculus in school yet? How much?

I've studied calculus in school many years ago but forgot some things. I have several learning gaps.

 

[Gavran]

The task was: find path of moving particle if only velocity is known. But as I understood it's impossible if we don't know how velocity is calculated (using limit).

If you are not allowed to use the standard approach $$ \vec s=\int_{a_1}^{b_1}\vec v(t)dt $$ try to solve the problem by using the Riemann sum which is an approximation of the integral. $$ \vec s\approx\sum_{i=1}^{n}\vec v(t_i^*)\Delta t_i $$ where $\Delta t_i=t_{i}-t_{i-1}$, $t_{i-1}\le t_i^*\le t_i$, $t_0=a_1$, $t_n=b_1$.

 

[DaveE]

https://www.khanacademy.org/math/ap...n-new/ab-8-2/v/motion-problems-with-integrals

 

[FactChecker]

You are making up the problem and saying that we are not allowed to use any facts. That makes it difficult.