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Roman55 [17]
3 years ago
5

A rabbit is traveling at a steady 6 m/s and (without knowing it) passes a wolf. The wolf takes off at the instant the rabbit pas

ses it, accelerating at a steady rate of 2.0 m/s^2. How much time elapses before the wolf is moving as fast as the rabbit? How far is the wolf from the rabbit when it reaches this speed?
Physics
1 answer:
Katena32 [7]3 years ago
5 0

Answer:

It takes the wolf 3 s to move as fast as the rabbit.

The wolf is 9 m from the rabbit when it reaches a speed of 6 m/s

Explanation:

The equations for the position and velocity of objects moving in a straight line are as follows:

x = x0 + v0 · t + 1/2 · a · t²

v = v0 + a · t

Where:

x = position of the object at time t

x0 = initial position of the object

t = time

v0 = initial speed

a = acceleration

v = velocity of the object at time t

For the first question, let´s use the equation of velocity of the wolf to find at which time its velocity is the same as the velocity of the rabbit ( 6 m/s):

v = v0 + a · t       (v0 = 0 because the wolf starts at rest)

6 m/s = 0 + 2.0 m/s² · t

t = 3 s

Now, with this calculated time, let´s obtain the position of the wolf:

x = x0 + v0 · t + 1/2 · a · t²      (Placing the center of the frame of reference at the point when the wolf starts running makes x0 = 0)

x = 1/2 · a · t²

x = 1/2 · 2.0 m/s² · (3 s)²

x = 9 m

Now, let´s calculate the position of the rabbit. Notice that a = 0. Then:

x = x0 + v · t      x0 = 0

x = v · t

x = 6 m/s · 3 s = 18 m

The wolf is (18 m - 9 m) 9 m from the rabbit when it reaches a speed of 6 m/s

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Calculate the average drift speed of electrons traveling through a copper wire with a crosssectional area of 80 mm2 when carryin
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Answer:

The correct answer is 2.8*10^{-5}ms^{-1}

Explanation:

The formula for the electron drift speed is given as follows,

u=I/nAq

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Using the information provided in the question we can see that the number of moles of copper atoms in a cm³ of volume of the conductor is 8.93/63.5 molcm^{-3}. Converting this number to m³ using very elementary unit conversion we get 140384molm^{-3}. If we multiply this number by the Avagardo number which is the number of atoms per mol of any gas , we get the number of atoms per m³ which in this case is equal to the number of electron per m³ because one electron per atom of copper contribute to the current. So we get,

n=140384*6.02*10^{23} = 8.45*10^{28}electrons.m^{-3}

if we convert the area from mm³ to m³ we get A=80*10^{-6}m^{2}.So now that we have n, we plug in all the values of A ,I ,q and n into the main equation to obtain,

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which is our final answer.

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Explanation:

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(a) The angular acceleration of the wheel is given by
\alpha =  \frac{\omega_f - \omega_i }{t}
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In our problem, the initial angular speed is zero (the wheel starts from rest), so the angular acceleration is
\alpha =  \frac{(11.2 rad/s) - 0}{3.07 s} =3.65 rad/s^2

(b) The wheel is moving by uniformly rotational accelerated motion, so the angle it covered after a time t is given by
\theta (t) = \omega_i t +  \frac{1}{2} \alpha t^2
where \omega_i = 0 is the initial angular speed. So, the angle covered after a time t=3.07 s is
\theta=  \frac{1}{2}  \alpha t^2 =  \frac{1}{2}(3.65 rad/s^2)(3.07 s)^2 = 17.2 rad
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