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siniylev [52]
3 years ago
5

If a single constant force acts on an object that moves on a straight line, the object's velocity is a linear function of time.

The equation v = v_i + at gives its velocity v as a function of time, where a is its constant acceleration. What if velocity is instead a linear function of position? Assume that as a particular object moves through a resistive medium, its speed decreases as described by the equation v = v_i - kx, where k is a constant coefficient and x is the position of the object. Find the law describing the total force acting on this object. (Enter an expression for the magnitude of the total force. Use the following as necessary: m, k, and v.)
Physics
1 answer:
olya-2409 [2.1K]3 years ago
5 0

Answer:

F=mkv

Explanation:

Given that

v = v_i - kx

We know that acceleration a given as

a=\dfrac{dv}{dt}

v = v_i - kx

\dfrac{dv}{dt}=\dfrac{dv_i}{dt}-k\dfrac{dx}{dt}

\dfrac{dv}{dt}=0-k\dfrac{dx}{dt}

We know that

F=m\dfrac{dv}{dt}

F=-mk\dfrac{dx}{dt}

F=-mkv

So the magnitude of force F

F=mkv

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A certain type of bird lives in two regions of a state. The distribution of weight for birds of this type in the northern region
Annette [7]

Answer: (a) Z-score are 1 and -1.2 for northern and southern regions, respectively.

Explanation: <u>Z-score</u> is how many standard deviations a data is from the population mean or how far a data point is from the mean.

The z-score is calculated by the following:

z=\frac{x-\mu}{\sigma}

where

x is the data point

μ is population mean

σ is standard deviation

For the <u>northern</u> <u>region</u> birds:

μ = 10, σ = 3, x = 13

z=\frac{13-10}{3}

z = 1

The z-score for birds living in the northern region is 1, which means it is 1 standard deviation <em>above the mean</em>.

For the southern region:

μ = 16, σ = 2.5, x = 13

z=\frac{13-16}{2.5}

z = -1.2

The z-score for southern living birds is -1.2, meaning it is 1.2 standard deviations <em>below the mean</em>.

6 0
3 years ago
A car accelerates uniformly from rest to 20 m/sec in 5.6 sec along a level stretch of road. Ignoring friction, determine the ave
bonufazy [111]

Answer:

(a) P=33000W

(b) P=51000W

Explanation:

The average power is defined as the amount of work done during a time interval:

P=\frac{W}{t}(1)

According to work-energy theorem, the work done is equal to the change in kinetic energy. So, we have:

W=\Delta K\\W=K_f-K_0\\W=\frac{mv_f^2}{2}-\frac{mv_0^2}{2}\\(2)

Recall that the weight is given by:

w=mg\\m=\frac{w}{g}(3)

The car accelerates uniformly from rest (v_0=0). Replacing (3) in (2), we have:

W=\frac{wv_f^2}{2g}

(a) Finally, we replace this in (1):

P=\frac{wv_f^2}{2gt}\\P=\frac{9000N(20\frac{m}{s})^2}{2(9.8\frac{m}{s^2})(5.6s)}\\P=33000W

(b)

P=\frac{14000N(20\frac{m}{s})^2}{2(9.8\frac{m}{s^2})(5.6s)}\\P=51000W

3 0
4 years ago
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Hope I helped! :P
5 0
3 years ago
We would like to use the relation V(t)=I(t)RV(t)=I(t)R to find the voltage and current in the circuit as functions of time. To d
drek231 [11]

Answer:

V = -RC (dV/dt)

Solving the differential equation,

V(t) = V₀ e⁻ᵏᵗ

where k = RC

Explanation:

V(t) = I(t) × R

The Current through the capacitor is given as the time rate of change of charge on the capacitor.

I(t) = -dQ/dt

But, the charge on a capacitor is given as

Q = CV

(dQ/dt) = (d/dt) (CV)

Since C is constant,

(dQ/dt) = (CdV/dt)

V(t) = I(t) × R

V(t) = -(CdV/dt) × R

V = -RC (dV/dt)

(dV/dt) = -(RC/V)

(dV/V) = -RC dt

∫ (dV/V) = ∫ -RC dt

Let k = RC

∫ (dV/V) = ∫ -k dt

Integrating the the left hand side from V₀ (the initial voltage of the capacitor) to V (the voltage of the resistor at any time) and the right hand side from 0 to t.

In V - In V₀ = -kt

In(V/V₀) = - kt

(V/V₀) = e⁻ᵏᵗ

V = V₀ e⁻ᵏᵗ

V(t) = V₀ e⁻ᵏᵗ

Hope this Helps!!!

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4 years ago
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