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
Ugo [173]
3 years ago
12

1. a) If a particle's position is given by LaTeX: x\:=\:4-12t\:+\:3t^2x = 4 − 12 t + 3 t 2(where t is in seconds and x is in met

ers), what is its velocity at LaTeX: t=1st = 1 s? b) Is it moving in the positive or negative direction of LaTeX: xx just then? c) What is its speed just then? d) Is the speed increasing or decreasing just then? (Try answering the next two questions without further calculations.) e) Is there ever an instant when the velocity is zero? If so, give the time LaTeX: tt ; if not, answer no. f) Is there a time after LaTeX: t=3st = 3 s when the particle is moving in the negative direction of LaTeX: xx? If so, give the time LaTeX: tt; if not, answer no. (Hint: Speed= LaTeX: \mid v\mid∣ v ∣)
Physics
2 answers:
IRINA_888 [86]3 years ago
5 0

Answer:

a) v=-6m/s

b) negative direction

c) 6m/s

d) decreasing

e) for t=2s

f) Yes

Explanation:

The particle position is given by:

x=4-12t+3t^2

a) the velocity of the particle is given by the derivative of x in time:

v=\frac{dx}{dt}=-12+6t

and for t=1s you have:

v=\frac{dx}{dt}=-12+6(1)^2=-6\frac{m}{s}

b) for t=1s you can notice that the particle is moving in the negative x direction.

c) The speed can be computed by using the formula:

|v|=\sqrt{(-12+6t)^2}=\sqrt{(-12+6)^2}=6\frac{m}{s}

d) Due to the negative value of the velocity in a) you can conclude that the speed is decreasing.

e) There is a time in which the velocity is zero. You can conclude that because if t=2 in the formula for v in a), v=0

v=0=-12+6(t)\\\\t=\frac{12}{6}=2

f) after t=3s the particle will move in the negative direction, this because it is clear that 4+3t^2 does not exceed -12t.

Readme [11.4K]3 years ago
4 0

Answer:

a)  v (1)  = -6 m/s

b) negative x-direction

c) s ( 1 ) = 6 m/s

d) The speed decreases at t increases from 0 to 2 seconds.

e) At t = 2 s, the velocity is 0

f) No

Explanation:

Given:-

- The position function of the particle:

                     x (t) = 4 - 12t + 3t^2

Find:-

what is its velocity at t = 1 s? (b) Is it moving in the positive or negative direction of x just then? (c) What is its speed just then? (d) Is the speed increasing or decreasing just then? (Try answering the next two questions without further calculation.) (e) Is there ever an instant when the velocity is zero? If so, give the time t; if not, answer no. (f) Is there a time after t = 3 s when the particle is moving in the negative direction of x? If so, give the time t; if not, answer no.

Solution:-

- The velocity function of the particle v(t) can be determined from the following definition:

                              v (t) = d x(t) / dt

                              v (t) = -12 + 6t

- Evaluate the velocity at time t = 1 s:

                              v (1) = -12 + 6(1)

                              v (1)  = -6 m/s

- The negative sign of the velocity at time t = 1s shows that the particle is moving in the negative x-direction.

- The speed ( s ( t )is the absolute value of velocity at time t = 1s:

                            s ( t ) = abs ( v ( t ) )

                            s ( 1 ) = abs ( v ( 1 ) )  

                            s ( 1 ) = abs ( -6 )

                            s ( 1 ) = 6 m/s

- The speed of the particle at time t = 0,

                            s ( t ) = abs ( -12 + 6t )

                            s ( 0 ) = abs (-12 + 6 (0) )  

                            s ( 0 ) = abs ( -12 )

                            s ( 0 ) = 12 m/s

- The speed of the particle at time t = 2,

                            s ( t ) = abs ( -12 + 6t )

                            s ( 2 ) = abs (-12 + 6 (2) )  

                            s ( 2 ) = abs (  0 )

                            s ( 2 ) = 0 m/s

- Hence, the speed of the particle decreases from s ( 0 ) = 12 m/s to s ( 2 ) = 0 m/s in the time interval t = 0 to t = 2 s.

- As the speed decreases as time increases over the interval t = 0 , t = 2 s the velocity v(t) also approaches 0, at time t = 2 s. s ( 2 ) = 0 m/s.

- We will develop an inequality when v (t) is positive:

                            v (t) = -12 + 6t > 0

                            6t > 12

                            t > 2

- So for all values of t > 2 the velocity of the particle is always positive.

You might be interested in
Who are a congressional representative's Constituents
charle [14.2K]
Benjamin Franklin, George Washington, and the brothers

4 0
3 years ago
What is the strength of the electric field between two parallel conducting plates separated by 1.00 cm and having a potential di
raketka [301]

Answer:

E=3.22*10^6 N/C

Explanation:

From the question we are told that:

Separation Distance d=1.0cm =0.01m

Potential difference V=3.22 * 10^4 V

Generally the equation for Electric Field strength is mathematically given by

 E=\frac{v}{d}

 E=\frac{3.22*10^4}{0.01}

 E=3.22*10^6 N/C

8 0
2 years ago
A mass of 80 g of KNO3 is dissolved in 100 g of water at 50 ºC. The solution is heated to 70ºC. How many more grams of potassium
slava [35]
Hi um i think its At 30 ° C your welcome
7 0
3 years ago
True or false:slow movements of mantle rock called radiation transfer heat in the mantle.
RUDIKE [14]
The best answer between the two options would be the second choice B) FALSE.
8 0
3 years ago
For a vehicle to negotiate a banked curve in poor weather conditions, where the force of friction f = 0, for a given velocity v
djverab [1.8K]

Answer:

R=240m

Explanation:

From the question we are told that:

Velocity v=25m/s

Force of friction f = 0

Angle \theta=15

Generally the equation for  Radius of curvature is mathematically given by

R=frac{v^2}{tan\theta *g}

R=frac{25^2}{tan 15 *9.81}

R=240m

7 0
3 years ago
Other questions:
  • 1) My 14V car battery could be used to charge my laptop, but I need to use an inverter to first convert it to a standard 120V. T
    13·1 answer
  • Explain why dogs pant during hot summer days using the concept of evaporation?
    14·1 answer
  • An electron falls through a distance d in a uniform electric field of magnitude E. Thereafter, the direction of the field is rev
    12·2 answers
  • Atoms of element A decay to atoms of element B with a half-life of 20,000 years. If there are 10,000 atoms of A to begin with (a
    6·2 answers
  • 8,000 mg + 2 g = _____________ mg?
    14·2 answers
  • Katie designed an experiment to show a water cycle process. The steps of the experiment are shown below.
    13·1 answer
  • The brakes of an automobile can decelerate it at -4.7m/s^2. If the automobile is traveling at the rate of 31.0m/s How far will i
    10·1 answer
  • An unfortunate bug splatters against the windshield of a moving car. Compared to the force of the car on the bug, the force of t
    11·1 answer
  • I really need help !!
    11·1 answer
  • If a child of mass 60.6 kg sits in a seat, what is
    6·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!