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emmainna [20.7K]
4 years ago
11

An electron has a constant acceleration of +3.3 m/s2. at a certain instant its velocity is +8.6 m/s. what is its velocity (a) 2.

3 s earlier and (b) 2.3 s later?
Physics
1 answer:
Citrus2011 [14]4 years ago
7 0
Hello!


The velocity function is:

\mathsf{V = V_0 + at}\\ \\ \mathsf{V = 8.6 +3.3t}


a) 2.3 s earlier, we can make t = -2.3 s, in relation to our initial time:

\mathsf{V = 8.6 + 3.3\cdot(-2.3)}\\ \\ \mathsf{V = 8.8-7.59}\\ \\ \boxed{\mathsf{V = 1.21 \ m/s}}

b) Now we can make t = 2.3 s:

\mathsf{V = 8.6 + 3.3\cdot2.3}\\ \\ \mathsf{V = 8.6 + 7.59}\\ \\ \boxed{\mathsf{V = 15.59 \ m/s}}
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Answer:

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Explanation:

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Given a particle that has the velocity v(t) = 3 cos(mt) = 3 cos (0.5t) meters, a. Find the acceleration at 3 seconds. b. Find th
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Answer:

a.\rm -1.49\ m/s^2.

b. \rm 50.49\ m.

Explanation:

<u>Given:</u>

  • Velocity of the particle, v(t) = 3 cos(mt) = 3 cos (0.5t) .

<h2>(a):</h2>

The acceleration of the particle at a time is defined as the rate of change of velocity of the particle at that time.

\rm a = \dfrac{dv}{dt}\\=\dfrac{d}{dt}(3\cos(0.5\ t ))\\=3(-0.5\sin(0.5\ t.))\\=-1.5\sin(0.5\ t).

At time t = 3 seconds,

\rm a=-1.5\sin(0.5\times 3)=-1.49\ m/s^2.

<u>Note</u>:<em> The arguments of the sine is calculated in unit of radian and not in degree.</em>

<h2>(b):</h2>

The velocity of the particle at some is defined as the rate of change of the position of the particle.

\rm v = \dfrac{dr}{dt}.\\\therefore dr = vdt\Rightarrow \int dr=\int v\ dt.

For the time interval of 2 seconds,

\rm \int\limits^2_0 dr=\int\limits^2_0 v\ dt\\r(t=2)-r(t=0)=\int\limits^2_0 3\cos(0.5\ t)\ dt

The term of the left is the displacement of the particle in time interval of 2 seconds, therefore,

\Delta r=3\ \left (\dfrac{\sin(0.5\ t)}{0.05} \right )\limits^2_0\\=3\ \left (\dfrac{\sin(0.5\times 2)-sin(0.5\times 0)}{0.05} \right )\\=3\ \left (\dfrac{\sin(1.0)}{0.05} \right )\\=50.49\ m.

It is the displacement of the particle in 2 seconds.

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Answer:

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Explanation:

I hope this helps. :)

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Answer:

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