Steven W. answered • 10/16/16
Tutor
4.9
(4,315)
Physics Ph.D., college instructor (calc- and algebra-based)
Hi Porcia!
I think you have correctly determined that, because the acceleration is only in the j-hat direction, the velocity in the i-hat direction is constant.
To get the velocity in the j-hat direction, we need to use the relationship that (instantaneous) velocity is the antiderivative of (instantaneous) acceleration. So, we need to integrate the acceleration expression (which only has the j-hat component) to get the j-hat component of velocity.
If you write 5√t as 5t1/2, then it may be easier to see that v(t) in the j-hat direction, by the power rule for integration, is (2/3)(5t3/2) + C, where C is a constant of integration that we can evaluate by looking at the case when t = 0. Since there is no j-hat component to velocity then, we must have C = 0 (you can also think of the antiderivative as a definite integral from 0 to t).
Then, just integrate that one more time, as you already did for the i-hat direction, to get the j-hat contribution to position as a function of time, realizing that the particle starts at the origin at t = 0 (which will take care of the constant of integration again).
Just let me know if you want to check any answers or have further questions about this!
Steven W.
tutor
Do you see how to do the integration to get from acceleration to velocity to displacement?
You already have the correct i-hat expression for velocity, and I worked out the j-hat direction, so the total velocity vector as a function of time is:
2i + [(10/3)t3/2]j
Does that make sense? Evaluating this at t = 0 gives:
v(0) = 2i + 0j = 2i, which is what the velocity is supposed to be there, so we are good.
Then, integrate this expression (which you already did correctly for the i-hat direction) to get the full position vector:
r(t) = 2ti + [(2/5)(10/3)t5/2]j + C (constant of integration).
At t = 0, the particle is said to be at the origin, which means 0i + 0j = 0 at t = 0
Evaluating r(0) = 0i + 0j + C, which needs to equal zero. Thus, C = 0 in this case, too.
so r(t) = 2ti +(4/3)t5/2
Does that hang together for you? Just let me know if you want to talk about this further.
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10/16/16
Porcia C.
No lol this problem just puzzled me
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10/16/16
Porcia C.
First answer is wrong
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10/16/16
Steven W.
tutor
I am pretty sure that is the correct procedure, so I am wondering if it is an answer formatting or answer rounding issue. With these online assignments, there can so often be problems unrelated to the physics.
Let me look over it again when I get home. But, with the information given, I am not sure what I would do differently.
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10/16/16
Porcia C.
Did you figure it out I'm puzzled
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10/16/16
Steven W.
tutor
I've gone through it again and, based on the information presented, I would not change my answers given above for the j-hat components for either v(t) or r(t). I'm sorry it's not working out, but, as far as I can tell, it should. If we could somehow sign on for a session so I could look at the submission page, I may have other ideas. But, short of that, I am not sure what else to do, because it looks like this is correct. Perhaps another tutor will have a different viewpoint and be able to help.
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10/16/16
Porcia C.
10/16/16