Why is it necessary to derive the given velocity

[Miliman13]

<Moderator's note: Moved from a technical forum and thus no template.>

1st time posting, be gentle.

Physics with calc 1

Im reviewing my exam which i did poorly on and can't understand why things are done, i have many questions but ill start with one, and since I am new maybe someone can tell me how to go about asking the other questions i have .

Question: an objects velocity is given V(t)=7.5t^2 +4
What is objects acceleration at time t=11so i understand the motions of equations how to reach one by integrating or deriving.
So far in lecture velocity was only ever given in terms of ex: 10m/s . so it caught me of guard seeing it this way.
i know how to solve, but i don't have the cognitive ability to understand WHY.

why can't i just plug in 11 for T and set equal to A

V(t)=V0+at a= v(t)-Vo/t ??

Thanks, calc, math isn't hard for me its the reading the short sentence and understandting how to apply the math and the logic behind it

 

[Orodruin]

V(t)=V0+at

This assumes that the acceleration is constant and is only applicable to that scenario. In the case you are given, acceleration is not constant.

 

[FactChecker]

The equation given is for velocity, so you can plug in t=11 to get the velocity, but that will not give you the acceleration.

Do you know the relationship between acceleration and velocity in terms of the derivative? If you can get the equation for acceleration, then you can plug t=11 into that to get the acceleration at time t=11.

PS. Nice car.

 

[Miliman13]

This assumes that the acceleration is constant and is only applicable to that scenario. In the case you are given, acceleration is not constant.

Thank you. I kind of still don't understand...
my course gets a "custom version of physics"
The professor is very amendment about not teaching in the traditional sense... He believes his way is superior... And its difficult... because while the internet and other resources are very similar; his is not. So i spend a lot of time confused.

 

[phinds]

Thank you. I kind of still don't understand...
my course gets a "custom version of physics"
The professor is very amendment about not teaching in the traditional sense... He believes his way is superior... And its difficult... because while the internet and other resources are very similar; his is not. So i spend a lot of time confused.

Velocity is the change in position as a function of time. What is acceleration in those terms?

 

[Miliman13]

Velocity is the change in position as a function of time. What is acceleration in those terms?

A(t)=A
So the derivative of V(t) is A(t).
How would it change if A= was constant
Could i simply solve for A with the velocity formula at that point..

 

[phinds]

A(t)=A
So the derivative of V(t) is A(t).
How would it change if A= was constant
Could i simply solve for A with the velocity formula at that point..

How could you solve for acceleration using a velocity formula when, as you just recognized, acceleration is the DERIVATIVE of velocity?

 

[Miliman13]

How could you solve for acceleration using a velocity formula when, as you just recognized, acceleration is the DERIVATIVE of velocity?

right i get that.
But the velocity form has T in it.
So V(T)=V0 + at
i thought you could rewrite it so a= delta V/t

Its just this is done already to solve for 2 missing variables when you don't use the 3rd equation of motion.
You set A or T equal to something from V(t) and plug into x(t).
...
I wish i could better convey what i mean..

the best thing i could say is the last 6 weeks ( minus the hurricane closes )
Have gone over my head dramatically.
I don't understand the concept of ( constant , Non constant= given value)
I don't understand why things get zeroed out in the equations.
I don't understand why I am being forbidden from using the 3rd equation of motion...( everywhere )

I really wish the university had a better option than the lesser of two evils.
Seriously almost the whole university student body agrees , we need better physics educators.

My tutors are his previose students... they feel my pain.

 

[FactChecker]

The 'T' in your equation means time and the 't' in the given equation also means time. So forget about T and use t.

Your equation is only for the situation where acceleration is a constant number, a. That is often not true. This problem gives you the specific equation for velocity: V(t) = 7.5t² + 4
Acceleration is always the derivative of velocity. Have you had calculus and know how to take the derivative of that equation? If so, do that and plug t=11 into the resulting equation.