Instantaneous speed and acceleration from x(t) = 3.70t² - 2.00t + 3.00

[greatest]

An object moves along the x-axis according to the equation x(t) = (3.70t^2 - 2.00t + 3.00) m. how do i find its
instantaneous speed at t = 1.70 s and at t = 3.20 s.

acceleration between t = 1.70 s and t = 3.20 s.


thank u. i just started calc 1. please help.

 

[Pyrrhus]

How's velocity and acceleration defined?

 

[Farsight]

Think about a graph here, greatest. You've got metres along one axis, and time along the other. Try drawing one. Now, what does the slope represent, and what's a derivative?

 

[greatest]

i didnt learn about derivative yet please help. please give me an example.

 

[arildno]

i didnt learn about derivative yet please help. please give me an example.

Yes, you have.
Do you know what it means to differentiate a function?

 

[greatest]

the graph is a parabola when i graphed it.

 

[Farsight]

It's all easy stuff when you get the hang of it, greatest. I hesitate to help you with this too much, because if you start flying ahead you might get bored with your coursework. But here's something from google:

http://simple.wikipedia.org/wiki/Differential_calculus

"The rate of change of the place of an object is the object's speed, so we can call the function of its speed at any time "speed(t)". The rate of change of speed is called acceleration. We can call the function "acceleration(t)". Mathematically, "speed(t)" is the derivative of "place(t)" and "acceleration(t)" is the derivative of "speed(t)".

 

[arildno]

Again:
What does it mean to differentiate a function?

 

[greatest]

another question i attached a graph and i just want to know how i can find the instataneous velocity at 3.3 second. Thanks for all the help. i am getting better.

 

[greatest]

i got 7.4t-2 for derivative what should i do now.

 

[arildno]

How is velocity, as a function of time, related to the position, also conceived of as a function of time?

 

[greatest]

velocity is the slope of poistion/time

 

[greatest]

can u help me set it up please.

 

[arildno]

velocity is the slope of poistion/time

Which is the same as saying that if you differentiate the position function with respect to time, you get the...?

 

[greatest]

i got it the dervaitve of the graph is 7.4t- 2 which equlas the velocity and then the acceleration is 7.4. thank u for all the help.

 

[arildno]

Remember to find the instantaneous speeds at the two prescribed moments!