# Kinematics in calculus

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• solarmidnightrose
In summary, a high-school student is learning calculus and struggling to understand the phrase "in the second second" in their textbook. They ask for clarification and receive helpful explanations about integrating acceleration and velocity over time to find distance. The student also realizes that using "second second" as a time interval can be confusing and decides to use a different example in the future.f

#### solarmidnightrose

hi, I'm a high-school student that is just beginning to learn calculus.
in calculus we are learning how to apply integration and diffrentiaiton methods regarding kinematics.

there is this certain phrase i do not really understand in our textbook: e.g."in the second second"
how am i meant to write "in the second second" when I'm integrating? It would be nice if you included an example.

thanks :)
Oh, and Please remember I am a high-school student that doesn't understand complex terminology yet.

Did you mean “meters per second” and “meters per second per second” but in another language translated to English?

In the first case of meters per second that is speed or velocity

In the second case of meters per second per second that is acceleration.

Integrating acceleration over time gets you the velocity and integrating velocity over time gets you distance.

there is this certain phrase i do not really understand in our textbook: e.g."in the second second"
how am i meant to write "in the second second" when I'm integrating? It would be nice if you included an example.

Could it mean this?

"in the first second" means $t=0{\rm\ s}$ to $t=1{\rm\ s}$. So, the displacement during the first second is $\int_0^1 v dt$
"in the second second" means $t=1{\rm\ s}$ to $t=2{\rm\ s}$. The displacement during the second second is $\int_1^2 v dt$
"in the third second" means $t=2{\rm\ s}$ to $t=3{\rm\ s}$, etc.

• berkeman
in the second second"

Could it mean this?

"in the first second" means t=0 to t=1 <snip>
I'm pretty sure that's what was intended. Writing "second second" is a little confusing, in that the first word is an ordinal (e.g., first, second,, third, etc.) while the next word is a time interval.

Could it mean this?

"in the first second" means $t=0{\rm\ s}$ to $t=1{\rm\ s}$. So, the displacement during the first second is $\int_0^1 v dt$
"in the second second" means $t=1{\rm\ s}$ to $t=2{\rm\ s}$. The displacement during the second second is $\int_1^2 v dt$
"in the third second" means $t=2{\rm\ s}$ to $t=3{\rm\ s}$, etc.
Thank You Soooooo Much 'robphy'! This makes soo much sense now :)

• berkeman
Did you mean “meters per second” and “meters per second per second” but in another language translated to English?

In the first case of meters per second that is speed or velocity

In the second case of meters per second per second that is acceleration.

Integrating acceleration over time gets you the velocity and integrating velocity over time gets you distance.

Thanks 'jedishrfu' :) Sorry if my description didn't make sense, but what you've said has also proved a useful reminder for myself.

I'm pretty sure that's what was intended. Writing "second second" is a little confusing, in that the first word is an ordinal (e.g., first, second,, third, etc.) while the next word is a time interval.

Yeah, you're right 'Mark44'. That was exactly what I meant.
I guess I did choose a confusing example to explain my confusion.