Vector algebra - The velocity is given by

[lilyE]

Homework Statement

The velocity of an object as a function of time is given by:

Vx(t) = 12t² - 5t + 40 m/s
Vy(t) = 5t - 30 m/s

What is position at 2 sec if the object has an initial position of x = 5 m and y = 8 m?
What is the instantaneous acceleration at 10 s?

Homework Equations

The Attempt at a Solution

I started by just plugging time (2 sec) into the equation to get the velocity and then writing that out in component form (V = Vxi + Vyj = 78i - 20j), but it asks for position/acceleration and I'm not entirely sure how to go about solving for that.

 

[Fredrik]

Take the derivative to get the acceleration. Integrate to get the position.

 

[Doc Al]

How are position, velocity, and acceleration related? Hint: Calculus!

 

[lilyE]

Thank you! I think I've got it now.