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3 years ago

14

What is the final velocity of a car that is originally traveling 12 m/s and then undergoes an acceleration of 2.3m/s squared for

a distance of 130m?

1 answer:

Katarina [22]3 years ago

3 0

To solve this problem we use the general kinetic equations.

We need to know the time it takes for the car to reach 130 meters.

In this way we have to:

$x(t) = x_0 + v_0t + 0.5at ^ 2$

Where

$x_0$ = initial position

$v_0$ = initial velocity

$a$ = acceleration

$t$ = time

$x(t)$ = position as a function of time

$130 = 0 + 12(t) + 0.5(2.3)t ^ 2$

$1.15t ^ 2 + 12t - 130$ .

We use the quadratic formula to solve the equation.

$t = \frac{-12 \± \sqrt {(12) ^ 2-4(1.15)(- 130)}}{2 (1.15)}$

t = 6.63 s and t = -17.1 s

We take the positive solution. This means that the car takes 6.63 s to reach 130 meters.

Then we use the following equation to find the final velocity:

$v_f = v_0 + at$

Where:

$v_f$ = final speed

$v_f = 12 +2.23(6.63)$

The final speed of the car is 27.25 m/s

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What other system/invention can you think of that uses Newton's Third Law of Motion in this way?

tatiyna

Answer: a simple example of this would be the strong man game that can be found at most theme parks and fairs

Explanation: in the game you use a hammer to strike a buzzer or bell this causes the game to react by shooting up a small object giving you Newton’s third law your action had an equal or opposite effect on the bell and object that shoots up

5 0

3 years ago

A Doppler blood flow unit emits ultrasound at 4.8 MHz. What is the frequency shift of the ultrasound reflected from blood moving

Vedmedyk [2.9K]

Answer:

1300 Hz

Explanation:

f' = Actual frequency = 4.8 MHz

f = Observed frequency

$v_r$ = Relative velocity of blood = 0.21 m/s

v = Velocity of ultrasound = 1540 m/s

From the Doppler effect formula we have

$f=f'\dfrac{v+v_r}{v-v_r}\\\Rightarrow f=4.8\dfrac{1540+0.21}{1540-0.21}\\\Rightarrow f=4.80130\ Hz$

Frequency shift is given by

$\Delta f=f-f'\\\Rightarrow \Delta f=4.8013-4.8\\\Rightarrow \Delta f=0.0013\ MHz=1300\ Hz$

The frequency shift in the sound is 1300 Hz

6 0

3 years ago

A computer is purchased for $2816 and depreciates at a constant rate to $0 in 8 years. Find a formula for the value, V , of the

marusya05 [52]

Answer:

The formula its $f(t) \ = \ - \ 352 \ \frac{\$ }{years} \ t \ + \ \$ \ 2816$
After 5 years, the computer value its $ 1056

Explanation:

<h3>Obtaining the formula</h3>

We wish to find a formula that

Starts at 2816. $f(0 \ years) \ = \ \$ \ 2816$
Reach 0 at 8 years. $f( 8 \ years) \ = \ \$ \ 0$
Depreciates at a constant rate. m

We can cover all this requisites with a straight-line equation. (an straigh-line its the only curve that has a constant rate of change) :

$f(t) \ = \ m\ t \ + \ b$ ,

where m its the slope of the line and b give the place where the line intercepts the <em>y</em> axis.

So, we can use this formula with the data from our problem. For the first condition:

$f ( 0 \ years ) = m \ (0 \ years) + b = \$ \ 2816$

$b = \$ \ 2816$

So, b = $ 2816.

Now, for the second condition:

$f ( 8 \ years ) = m \ (8 \ years) + \$ \ 2816 = \$ \ 0$

$m \ (8 \ years) = \ - \$ \ 2816$

$m = \frac{\ - \$ \ 2816}{8 \ years}$

$m = \frac{\ - \$ \ 2816}{8 \ years}$

$m = \ - \ 352 \frac{\$ }{years}$

So, our formula, finally, its:

$f(t) \ = \ - \ 352 \ \frac{\$ }{years} \ t \ + \ \$ \ 2816$

<h3>After 5 years</h3>

Now, we just use <em>t = 5 years</em> in our formula

$f(5 \ years) \ = \ - \ 352 \ \frac{\$ }{years} \ 5 \ years \ + \ \$ \ 2816$

$f(5 \ years) \ = \ - \$ \ 1760 + \ \$ \ 2816$

$f(5 \ years) \ = $ \ 1056$

4 0

4 years ago

The air within a piston equipped with a cylinder absorbs 565 J of heat and expands from an initial volume of 0.12 L to a final v

Alenkinab [10]

Answer:

The change in internal energy of the air within the piston is 490 J.

Explanation:

In thermodynamics the internal energy (ΔU) of a system is the total energy contained in the system and can be considered as the sum of the energy in the form of heat (q, given to or released by the system) and in the form of work (w, make by the system to the environment or from the environment to the system). When the system absorbs heat from the enviroment this value is positive, while when the system realeased heat to the enviroment, the value is negative. In the case of work, when the enviroment make work on the system, the value is positive and, on the contrary, when the system makes work against the environment the value is negative.

ΔU = q + w

w is defined as the negative product between the external pressure (P) and the change in volume (ΔV). [w = - P·ΔV]

⇒ ΔU = q - P·ΔV

In this problem, the system is composed by the cylinder + piston + contained air (Attached)

1) q= 565 J (a positive value because the enviroment delivered heat to the cylinder)

2) P = 1 atm.

3) ΔV = 0.86 atm.L - 0.12 atm.L = 0.74 atm.L.

⇒ ΔU = q + w ⇒ ΔU = 565 J - (1 atm)·(0.74 L) ⇒ ΔU = 565 J - 0.74 atm.L

We have to express the work value in the same units of heat, it means Joules. As one joule is equal to 0.00987 atm.L

⇒ (0.74 atm.L) x ( 1 J/0.00987 atm.L) = 74.97 J.

⇒ ΔU = q + w ⇒ ΔU = 565 J - 74.97 J ⇒ ΔU = 490 J.

Summarizing, the change in internal energy of the air within the piston is 490 J.

3 0

3 years ago

The disk rotates about a fixed axis through point O with a clockwise angular velocity ω0 = 16 rad/s and a counterclockwise angul

Lapatulllka [165]

Answer:

V = 4.48m/s a = 1.57m/s²

Explanation:

ω₀ = 16rad/s

α₀ = 5.6rad/s²

r = 280mm = 0.28m

a = ?

v = ?

Angular velocity (ω₀) = velocity of acceleration / length of path

ω₀ = v / r

V = ω₀ * r

V = 16 * 0.28

V = 4.48m/s

Acceleration = ?

Angular acceleration α₀ = angular velocity (ω) / time take (t)

α₀ = ω / t .... equation i

But acceleration (a) = velocity (v) / time (t)

a = v / t

t = v / a

Put t = v / a into equation i

α₀ = ω / (v / a)

α₀ = ω * a / v

α * v = ω * a

a = (α * v) / ω

a = (5.6 * 4.48) / 16

a = 1.568m/s²

a = 1.57m/s²

3 0

3 years ago