How can I find the velocity and acceleration of a particle in 2-dimensions?

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AI Thread Summary
To find the velocity and acceleration of a particle in two dimensions, the position vector is given as r = (7.40 i - 6.60t² j) m. The velocity can be derived by differentiating the position vector with respect to time, resulting in v = (0 i - 13.20t j) m/s. The acceleration is found by differentiating the velocity, yielding a = (0 i - 13.20 j) m/s², indicating constant acceleration in the j-direction. For part (b), at t = 2.00 s, the position is r = (7.40 i - 26.40 j) m and the velocity is v = (0 i - 26.40 j) m/s. Understanding these calculations involves recognizing the definitions of instantaneous velocity and acceleration as derivatives of position with respect to time.
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Homework Statement


The vector position of a particle varies in time according to the expression r = (7.40 i - 6.60t2 j) m.
(a) Find expressions for the velocity and acceleration as functions of time. (Use t, i, and j as necessary.)
v =
a =
(b) Determine the particle's position and velocity at t = 2.00 s.
r =
v =


Homework Equations


kinematic of 2-dimen
r= v/t

The Attempt at a Solution


I found (b) r.. but i have no clue how to start part (A), i thought since R = V/t then
r =(7.40i - 6.60t^2)/ t but that was wrong.. so I'm thinking that r should be change into something. Any help would be great
 
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What is the definition of Velocity and Acceleration with respect to distance and time?
 
r/t is average velocity. your trying to find the instaneous rate of change. which means its time to put that calc 1 to use!
 

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