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
oee [108]
3 years ago
9

Starting from rest, a particle moving in a straight line has an acceleration of a = (2t - 6) m/s^2, where t is in seconds. What

is the particle's velocity when t = 6 s, and what is its position when t = 11 s?
Physics
1 answer:
hjlf3 years ago
6 0

To solve this problem we will use the given expression and derive it in order to find the algebraic expressions of velocity and position. These equations will be similar to those already known in the cinematic movement but will be subject to the previously given function. We start deriving the equation for velocity

a = 2t-6

\frac{dv}{dt} = 2t-6

Integrate acceleration equation

\int dv = (2t-6)dt

v = 2(\frac{t^2}{2})-6t+C_1

v=t^2-6t+C_1

At t = 0, v = 0

Replacing,

0 = 0^2-6*0+C_1

Therefore the value of the first Constant is

C_1 = 0

The expression can be escribed as,

v = t^2-6t

Calculate the velocity after 6s,

v=t^2-6t

v = 6^2-6*6

v = 0m/s

Now using the same expression we can derive the equation for distance

v = t^2-6t

\frac{dx}{dt} =t^2-6t

\int dx = \int (t^2-6t)dt

x = \frac{t^3}{3}-6\frac{t^2}{2}+C_2

At t=0, x=0

0 = \frac{0^3}{3}-6(\frac{0^2}{2})+C_2

Therefore the value of the second constant is

C_2 = 0

x = \frac{t^3}{3}-\frac{6t^2}{2}

Calculate the distance traveled after 11 s

At  t=11s

x = \frac{11^3}{3}-6(\frac{11^2}{2})

x = 80.667m

You might be interested in
un tanque de gasolina de 40 litros fue llenado por la noche, cuando la temperatura era de 68 grados farenheit. Al dia siguiente
Sedaia [141]

Answer:

Volume of gasoline that expands and spills out is 1.33 ltr

Explanation:

As we know that when temperature of the liquid is increased then its volume will expand and it is given as

\Delta V = V_o\gamma \Delta T

here we know that

V_o = 40 Ltr

volume expansion coefficient of the gasoline is given as

\gamma = 950 × 10^{–6}

change in temperature is given as

\Delta T = (131 - 68) \times \frac{5}{9}

\Delta T = 35 ^oC

Now we have

\Delta V = 40(950 \times 10^{-6})(35)

\Delta V = 1.33 Ltr

3 0
3 years ago
At what depth of lake water is the pressure equal to 201kpa?
Alex787 [66]

Answer:

20m

Explanation:

Pressure = pgh

p = density of water 1000

kg/m^3

g = acceleration due to gravity 9.81 m/s^2

h is the depth of water

Pressure = 201 kPa = 201 x 10^3 Pa

201 x 10^3 = 1000 x 9.81 x h

201 x 10^3 = 9810h

h = 20.49 m

Approximately 20 m

5 0
3 years ago
What is the mass of a ball that has 29j of potential energy and is lifted 2.0m?​
Salsk061 [2.6K]

Answer:

1.48kg

Explanation:

Here,

potential energy (P.E) = 29j

height (h) = 2m

acceleration due to gravity(g) =

9.8m {s}^{ - 2}

mass(m) = ?

we know,

P.E = mgh

or, 29 = m×9.8×2

or, 29/19.6 = m

or,m = 1.48kg

6 0
2 years ago
A device for exercising the upper leg muscle is shown above, together with a schematic representation of an equivalent lever sys
yuradex [85]

yo mamaaaaaaaaaaaaaaa

4 0
3 years ago
How to solve 30(a)<br><br> Give solution asap.
expeople1 [14]

Answer:

They will not meet

h-hX=1.2*g*t²

hX=v0*t-(1/2*g*t²)

Explanation:

fall h=1/2*g*t²

elevation time if v0=20 m/s  te=v0/g=20 m/s /9.81 m/s²=2.0387s

hmax=v0²/(2*g)=(400 m²/s²)/19.62 m/s²2=20.387 m

free fall

t=2.0387s yields hX=1/2*g*t²=20.387 m

h-hX=200m - 20.387 m=179,613 m.

so, the second body has not enough initianoal speed to reach a meeting point

5 0
3 years ago
Other questions:
  • An instrument is defective for all of the following conditions EXCEPT:_______
    10·1 answer
  • The pulse site located at the point where the upper leg bends is called the
    5·1 answer
  • A(n) 82.7 kg boxer has his first match in the Canal Zone with gravitational acceleration 9.782 m/s 2 and his second match at the
    11·1 answer
  • A speedboat initially at rest accelerates at 4.0 m/s (squared) for 7.0 s. How far does the speedboat move in 7.0 s?
    6·1 answer
  • Heat transfers energy from a hot object to a cold object. Both objects are isolated from their surroundings. The change in entro
    5·1 answer
  • Question 4 of 10 (1 point) Jump to Question: Choose the word that best completes this sentence. A personal fall arrest system is
    10·2 answers
  • QUESTION 7
    8·1 answer
  • A new prototype cup has been designed to keep liquids, such as hot coffee or cold annk, near their original temperature for long
    8·1 answer
  • Suppose a nonconducting sphere, radius r2, has a spherical cavity of radius r1 centered at the sphere's center. Assuming the cha
    7·1 answer
  • 3. Discuss the main purpose of Experiment" Explain the greatest advantage of experiment in psychology?
    13·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!