Question

An object, which is at the origin at time , has initial velocity and constant acceleration?
No clue how to do this. help please.
An object, which is at the origin at time t=0, has initial velocity V0= (-14.0i - 7.0j)m/s and constant acceleration a=(6.0i + 3.0j)m/s^2..

Find the position x where the object comes to rest (momentarily).
Express your answer in terms of the unit vectors i and j.

r= _____m????

the i's and j's are considered hats so ihat and jhat...

Answer 1

i assume we can take the acceleration and integrate it into velocity:

a(t) = <6,3>

v(t) = <(6t+C),(3t+C)>; where v(0) = <-14,-7>

v(t) = <(6t-14),(3t-7)>

Now when the velocity = 0, the things stops moving. And that happens when t=7/3, now that we have a time we can calculate this for a position as well by integrating v(t)

p(t) = < (3t^2-14t+C) , ((3/2)t^2-7t+C) >

from here I would have to assume that p(0) = 0 since it is not stated to be anything that we can calculate. As such, this reduced our vector function to:

p(t) = < (3t^2-14t) , ((3/2)t^2-7t) > where t = 7/3

p(7/3) = < -49/3 , -49/6 >

but i am not quite sure about the end results; hmm ....