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Expert: - 11/12/2010


Question

Physics
Hey,

I have a test early tomorrow morning and I'm doing review
questions but I just don't know how to do this one question.
If you are able to answer it I'd really appreciate a
solution as soon as you can.

A 6.0 kg toy car can move along an x axis; Figure gives Fx
of the force acting on the car, which begins at rest at time
t=0. The scale on the Fx axis is set by Fxs = 3.0 N. In
unit-vector notation, what is p at (a)t = 7.0 s and (b)t =
2.0 s,(c) what is v at t = 6.0 s?

I have to give the 3 answers in i j and k components.

I attached an image of the problem diagram to this question.

Thanks so much,
Mike

Answer
Mike
You haven't told me what p is, so I will solve for acceleration, velocity and distance.  If I understand correctly, the force is always along the x axis so we only have to find the i component.  Set up the problem in time steps.  We know a = F/m from Newton's law.  We know velocity is the time integral of acceleration.  And displacement is the time integral of velocity.  I am using int as the integral operator.

0 - 2 sec
F = 6t/2 N
a = F/m = t/2  m/s^2
v = int(a dt) = t^2/4 = 1 m/s at time t = 2 sec
s = int(t^2 /4 dt) = t^3/12 = 8/12 m at 2 sec

2 - 4 sec
F = 6
a = 1
v = vo + int(dt) = 1 + 4 - 2 = 3 at 4 sec
(you can find distance)

4 - 6 sec
F = 6 - 3(t-4) = 18 - 3t
a = 3 - t/2
v = vo + int((3-t/2)dt) = 3 + (3t-t^2/4) = 4 at 6 sec

6 - 7 sec
F = 18 - 3t
a = 3 - t/2
v = 4 + int((3-t/2)dt) = 3.75 at 7 sec

I hope my arithmetic is correct.
Paul

Paul Soderman

Expertise

Aeronautics, Fluid Mechanics, Aeroacoustics, Noise Control, Muffler Design, Wind Tunnel Research.... I know nothing about India - do not ask about schools, jobs, application requirements, career choices, etc. for India. Please, no text message verbiage; I prefer full words in full sentences. Thanks.

Experience

38 years as research engineer at NASA

Publications
AIAA, NASA

Education/Credentials
B.S. and M.S. Aeronautical Engineering - U. of Washington Graduate work Standford U.

Awards and Honors
AIAA Associate Fellow (American Institute of Aeronautics and Astronautics)

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