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
Anit [1.1K]
3 years ago
6

The function ​s(t)=−t3+3t+3 gives the distance from a starting point at time t of a particle moving along a line. Find the veloc

ity and acceleration functions. Then find the velocity and acceleration at t=0 and t=1. Assume that time is measured in seconds and distance is measured in centimeters. Velocity will be in centimeters per second​ (cm/sec) and acceleration in centimeters per second per second ​(cm/sec2​).
Physics
1 answer:
Licemer1 [7]3 years ago
5 0

Answer:

v(t)=3t²+3, and a(t)=6t

v(0)=3cm/sec, and a(0)=0cm/sec²

v(1)=6cm/sec, and a(1)=6cm/sec²

Explanation:

<u>Find velocity and acceleration functions ( v(t) and a(t) )</u>

(Relevant background: Let's say f(t) is a function of y with respect to x. Think of the derivative of this function, f'(t) , as representing the rate at which y changes with respect to x)

s(t) is a function of distance with respect to time. Therefore, s'(t) - the derivative of this - represents the rate at which distance changes with time, which is just the definition of velocity. So we can say velocity v(t) = s'(t).

s(t)=t³+3t+3

s'(t)=v(t)=3t²+3

Similarly, if v(t) is a function of speed with respect to time, then v'(t) represents the rate at which speed changes with time, which is acceleration. So we can say that acceleration a(t)=v'(t)=s''(t)

v(t)=3t²+3

v'(t)=a(t)=6t

<u>Find velocity and acceleration at t=0 and t=1</u>

<u>t=0</u>

v(t)=3t²+3

v(0)=3(0²)+3

v(0)=3 cm/sec

a(t)=6t

a(0)=6(0)

a(0)=0 cm/sec²

<u>t=1</u>

v(t)=3t²+3

v(1)=3(1²)+3

v(1)=3+3

v(t)=6 cm/sec

a(t)=6t

a(1)=6(1)

a(1)=6 cm/sec²

You might be interested in
A parallel plate capacitor has circular plates with diameter D=21.5 cm separated by a distance d=1.75 mm. When a potential diffe
OLga [1]

Answer:E=2.078\times 10^{-10} J/cm^3

Explanation:

Given

Diameter(D)=21.5 cm

distance between plate=1.75 mm

and we know capacitance is

C=\frac{\epsilon _0A}{d}

and we know charge is

Q=CV

and charge density (\sigma [tex])[tex]=\frac{Q}{A}=\frac{\epsilon _0AV}{Ad}=\frac{\epsilon V}{d}

Electric field(E)=\frac{\sigma }{\epsilon _0}

Energy density=\frac{1}{2}\epsilon _0E^2

Energy desity=\frac{4\pi \epsilon _0}{8\pi }\frac{V^2}{d^2}

Energy desity=\frac{1}{8\pi \cdot 9\times 10^9}\times \left [ \frac{12\times 10^3}{1.75}\right ]^2

E=2.078\times 10^{-10} J/cm^3

3 0
3 years ago
Three dogs are fighting over a bone. One is pulling to the left with a force of 20N, another
Len [333]

Answer:

<em>Net force = 21.12 N</em>

<em>angle for the force α = 45°</em>

Explanation:

<em>In this problem, we will take the left as the negative x-axis, the right as the positive x-axis, and the upward direction as the positive y-axis.</em>

The 20 N force to the left has an x component of -20 N, and y component of 0 N

The 35 N force to the right has a x component of 35 N, and a y component of 0 N

The 15 N upwards has an x component of 0 N, and a y component of 15 N

We resolve the forces into the x and y components.

for the x component Fx

Fx = -20 + 35 + 0 = 15 N

For the y component Fy

Fy = 0 + 0 + 15 = 15 N

Net force Fn = \sqrt{Fx^{2} + Fy^{2}  }

Fn = \sqrt{(15)^{2} + (15^{2} ) }

<em>Net force Fn = 21.21 N</em>

for the angle,

tan\alpha = \frac{Fy}{Fx} = \frac{15}{15}

tan\alpha = 1

α = tan^{-1} 1

<em>angle for force α = 45°</em>

8 0
3 years ago
What causes an ion to have a net negative charge
nata0808 [166]
It is charged because the number of electrons do not equal the number of protons in the atom or molecule. ... When an atom is attracted to another atom because it has an unequal number of electrons and protons, the atom is called an ION. If the atom has more electrons than protons, it is a negative ion, or ANION.
5 0
3 years ago
What kind of energy is stored when you squeeze a mattress
KengaRu [80]

Answer:

elastic energy

Explanation:

hope it helps you

7 0
2 years ago
Read 2 more answers
Which of the following is a Nobel gas?<br> Ba2+<br> OA<br> OB. Ci<br> Kr<br> Ос.<br> Ca<br> D.
stepan [7]

Answer:

Kr

Explanation:

the element that is in group 18 is noble gasses. the elements are helium (He), neon (Ne), argon (Ar), krypton (Kr), xenon (Xe), radon (Rn), and oganesson (Og).

5 0
3 years ago
Other questions:
  • What is the relationship between the planets and other astronomical bodies?
    10·1 answer
  • The initial speed of a cannon ball is 200 m/s. If the ball is to strike a target that is at a horizontal distance of 3.0 km from
    13·1 answer
  • What is the main function of an ignition safety switch?
    5·1 answer
  • What is period and frequency
    9·1 answer
  • Two 1.0 kg masses are 1.0 m apart (center to center) on a frictionless table. Each has a +10μC of charge. a) What is the magnitu
    15·1 answer
  • Mrs. Harper can't find her car in the school parking lot. She is lost
    7·1 answer
  • Renewable energy has no disadvantages. True or False
    14·2 answers
  • 1) Little Timmy wants to measure how tall his house is. He doesn’t have a tape measure but does have a stopwatch. He recruits Bi
    7·1 answer
  • If the child pulls with a force of 20 N for 12.0 m , and the handle of the wagon is inclined at an angle of 25 ∘ above the horiz
    14·1 answer
  • Compare and contrast the electric forces with the gravitational force.
    9·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!