1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
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.

You might be interested in
5. It is the year 2085, and the world population has grown at an alarming rate. As a space explorer, you have been sent on a ter
shtirl [24]

Answer:

Answer:

It has sunlight, oxygen, water, and fertile soil.

Explanation:

Sunlight: provides plants (producers) with energy so that the ecosystem is sustainable. Also provides heat and warmth so the planet does not freeze.  

Oxygen: obvious. required for human survival and survival of most carbon-based organisms.

Water: required for plant growth and sustainability of carbon-based life.

Fertile soil: a place where plants can grow and produce energy.

I will not write an entire description because your teacher may accuse you of plagiarism and use this topic as proof.

Explanation:

3 0
3 years ago
Read 2 more answers
Describe all the ways that newtons laws can apply in a car crash
Harman [31]
Newtons first law - Objects in the car at rest (The human) will remain at rest unless affected by an unbalanced force. Well the unbalanced force would be the crash and this would set the human in motion and they would ether fly out the car if not wearing a seat belt or if wearing one they would get bad whip lash

Newtons second law - With more mass requires more force, so since the human is pretty light or even if heavy in a big crash there will be so much more from it that this will send the human flying.

Newtons 3rd law - Objects A puts force onto objects b and object b excretes the same amount of force back onto object a, so in a crash the human would hit the car hard and the car would excrete the same amount of force back on the human which would really damage him/her
7 0
3 years ago
The SI unit of average spped and velocity.​
Verdich [7]

<em>meter per</em><em> </em><em>second</em><em> </em><em>is </em><em>the </em><em>main </em><em>answer </em><em>of</em><em> </em><em>both</em>

3 0
2 years ago
A kangaroo jumps to a vertical height of 2.8 m. How long was it in the air before returning to earth
BaLLatris [955]
The answer would be 2.8m height on earth takes 
2.8=1/2*9.8*t^2 => <span>s = ut +1/2at^2 </span>
8 0
3 years ago
Which action describes an experimental investigation?
EastWind [94]
I think the answer is c
3 0
3 years ago
Other questions:
  • In a motor, the combined effect of electric currents and magnetic forces turn electrical energy into which of the following?
    6·1 answer
  • A red ball is thrown down with an initial speed of 1.1m/s from a height of 28 meters above the ground. Then 0.5 seconds after th
    5·1 answer
  • you push your little sister on a swing and in 1.6 minutes you make 52 pushes what is the frequency of your swing? answer in unit
    9·1 answer
  • A car travels forward with constant velocity. It goes over a small stone, which gets stuck in the groove of a tire. The initial
    11·1 answer
  • 1) A box is 16m long, 28m broad and 10m high.what is the volume of 100 similar boxes?2)When was S.I unit introduced? (3)0How man
    5·1 answer
  • A roller coaster car moving at a velocity of 30 meters/second has a momentum of 2.5 _ 104 kilogram meters/second. What is its ma
    15·1 answer
  • B. A car is moving 4.0 m/s to the right. The car begins to accelerate at a rate of 1.5 m/s/s, to the right. After
    10·1 answer
  • What force (in N) must be exerted on the master cylinder of a hydraulic lift to support the weight of a 2100 kg car (a large car
    14·1 answer
  • Is weather chart the same as aneroid barometer?​
    8·1 answer
  • Latency refers to the 27 seconds of time it takes for someone to refocus on driving after they finish texting or talking on the
    5·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!