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GuDViN [60]
3 years ago
9

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

e displacement at 2 seconds.
Physics
1 answer:
DiKsa [7]3 years ago
7 0

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:

1 : 2 cm/km  or \frac{1}{2} \, \frac{cm}{km}

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4 0
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What is the velocity of an 80 kg person skating across the ice with a kinetic energy of 16, 000 joules?
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Answer:

V = 20 m/s

Explanation:

Given the following data;

Mass = 80kg

Kinetic energy = 16,000 joules

To find the velocity;

Kinetic energy can be defined as an energy possessed by an object or body due to its motion.

Mathematically, kinetic energy is given by the formula;

K.E = \frac{1}{2}MV^{2}

Where;

K.E represents kinetic energy measured in Joules.

M represents mass measured in kilograms.

V represents velocity measured in metres per seconds square.

Substituting into the formula, we have;

16000 = ½*80*V²

16000 = 40V²

V² = 16000/40

V² = 400

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Answer:

<u>Very low</u>

<u>Explanation:</u>

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Answer:

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Explanation:

Though the diagram that is mentioned in the questions is not given. I have given general information related to the Earth's magnetic axis with respect to geographic/rotational axis.

Axis is an imaginary line around which a body rotates. The rotational axis of the Earth enters into and exits from the Earth at two points namely: North and South pole.

We know that the Earth behaves like a huge bar magnet so just like the bar magnet it must also have magnetic axis and poles. Earth has north magnetic pole and south magnetic pole. It has a strong magnetic field as well known as magnetosphere.

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