Vector algebra - The velocity is given by

AI Thread Summary
The discussion focuses on calculating the position and instantaneous acceleration of an object given its velocity functions Vx(t) and Vy(t). To find the position at 2 seconds, the velocity components must be integrated, starting from the initial position of x = 5 m and y = 8 m. For instantaneous acceleration at 10 seconds, the velocity functions should be differentiated. The relationship between position, velocity, and acceleration is emphasized, highlighting the need for calculus in solving these problems. The participant expresses confidence in understanding the process after initial confusion.
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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.
 
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Take the derivative to get the acceleration. Integrate to get the position.
 
How are position, velocity, and acceleration related? Hint: Calculus!
 
Thank you! I think I've got it now.
 
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