- #1
asap9993
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Homework Statement
Here's the problem:
Suppose the acceleration of a particle is a function of x, where a(x) = (1.8 s^-2)x.
a) If the velocity is zero when x = 1.0 m, what is the speed when x = 2.9 m?
b) How long does it take the particle to travel from x = 1.0 m to x = 2.9 m?
Homework Equations
a = dv/dt
v = dx/dt
The Attempt at a Solution
I managed to figure out how to do part a.
a = dv/dt
(dt/dx)a = (dv/dt)(dt/dx)
Since v = dx/dt, the above equation becomes
a(1/v) = dv/dx which becomes
a dx = v dv.
Integrating both sides gives you
v^2 = (1.8s^-2)(x^2) + C (s is seconds)
Since v = 0 when x = 1.0 meters, C = -(1.8s^-2)(m^2) (m is meters)
So the final function is v^2 = (1.8s^-2)(x^2) - (1.8s^-2)(m^2)
Plugging in x = 2.9 m, gives 3.65 m/s which is the correct answer.
I can't figure out part b. I tried using the same approach as in part a to find a "time function" :
v = dx/dt so
dt = (1/v) dx
However. when I integrate this, it doesn't give me the correct answer which is 1.29 s.
Can anyone please help me?