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3 years ago

An object moves with velocity v(t)=t^2-8t+7

1 answer:

6 0

<span>a) write a polynomial expression for the position of the particle at any time t greater or equal to zero.
</span>Position is found by integrating velocity:

<span>s(t) = (t^3)/3 - 4t^2 + 7t + c
</span>where c is a constant corresponding to the position at t=0. <span>

b) at what time(s) is the particle changing direction
</span>the particle changes direction whenever the velocity is zero; the velocity function equals

<span>(t-1)(t-7) a difference of squares so the zeros are 1 and 7, it changes direction at 1 second and 7 seconds. </span><span>

c) find the total distance traveled by the particle from t=0 and t=4
</span><span>s(0) = c
s(1) = 8/3 + c
s(4) = 64/3 - 64 + 28 + c.
</span>
from 0 to 1 the particle travels 8/3 units. From 1 to 4 it travels -(64/3 - 36 - 8/3) = (-(56/3 - 108/3))
<span>=-(-52/3) = 52/3 units
</span>
<span>so in total it travels 52/3 + 8/3 =20 units</span>

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A circuit contains four capacitors in parallel (10 F, 3 F, 7 F, and 1 F). What is the equivalent capacitance of this circuit?

Oxana [17]

The equivalent capacitance ( $C_{eq}$ ) of an electrical circuit containing four capacitors which are connected in parallel is equal to: A. 21 F.

<h3>The types of circuit.</h3>

Basically, the components of an electrical circuit can be connected or arranged in two forms and these are;

Series circuit

Parallel circuit

<h3>What is a parallel circuit?</h3>

A parallel circuit can be defined as an electrical circuit with the same potential difference (voltage) across its terminals. This ultimately implies that, the equivalent capacitance ( $C_{eq}$ ) of two (2) capacitors which are connected in parallel is equal to the sum of the individual (each) capacitances.

Mathematically, the equivalent capacitance ( $C_{eq}$ ) of an electrical circuit containing four capacitors which are connected in parallel is given by this formula:

Ceq = C₁ + C₂ + C₃ + C₄

Substituting the given parameters into the formula, we have;

Ceq = 10 F + 3 F + 7 F + 1 F

Equivalent capacitance, Ceq = 21 F.

Read more equivalent capacitance here: brainly.com/question/27548736

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2 years ago

When designing a user interface, the most important information should be placed in the ______ of the screen.

musickatia [10]

Answer:

upper-left corner

Explanation:

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3 years ago

Which term describes an advantage of wind energy?

atroni [7]

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3 years ago

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A linear accelerator produces a pulsed beam of electrons. The pulse current is 0.50 A, and the pulse duration is 0.10 μs. (a) Ho

Crank

Answer:

a)N = 3.125 * 10¹¹

b) I(avg) = 2.5 × 10⁻⁵A

c)P(avg) = 1250W

d)P = 2.5 × 10⁷W

Explanation:

Given that,

pulse current is 0.50 A

duration of pulse Δt = 0.1 × 10⁻⁶s

a) The number of particles equal to the amount of charge in a single pulse divided by the charge of a single particles

N = Δq/e

charge is given by Δq = IΔt

so,

N = IΔt / e

$N = \frac{(0.5)(0.1 * 10^-^6)}{(1.6 * 10^-^1^9)} \\= 3.125 * 10^1^1$

N = 3.125 * 10¹¹

b) Q = nqt

where q is the charge of 1puse

n = number of pulse

the average current is given as I(avg) = Q/t

I(avg) = nq

I(avg) = nIΔt

= (500)(0.5)(0.1 × 10⁻⁶)

= 2.5 × 10⁻⁵A

C) If the electrons are accelerated to an energy of 50 MeV, the acceleration voltage must,

eV = K

V = K/e

the power is given by

P = IV

P(avg) = I(avg)K / e

$P(avg) = \frac{(2.5 * 10^-^5)(50 * 10^6 . 1.6 * 10^-^1^9)}{1.6 * 10^-^1^9}$

= 1250W

d) Final peak=

P= Ik/e

= $= P(avg) = \frac{(0.5)(50 * 10^6 . 1.6 * 10^-^1^9)}{1.6 * 10^-^1^9}\\2.5 * 10^7W$

P = 2.5 × 10⁷W

5 0

3 years ago

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A plucked violin string carries a traveling wave given by the equation f(x,t)=asin[b(x−ct)+ϕi], with a = 0.00580 m , b = 33.05 m

Viktor [21]

Answer:

A) Φ = 0 , B) T = 7.76 s

Explanation:

A) to find the value of the phase constant replace the value

0 = a sin (b (0- 0) + Φ)

0 = sin Φ

Φ = sin⁻¹ 0

Φ = 0

B) the period is defined by time or when the movement begins to repeat itself

So that the sine function is repeated when the angle passes 2pi

b (x- ct) = 2pi

If we are at a fixed point x = 0

b c t = 2pi

t = 2π / bc

Let's calculate

T = 2π / (33.05 245)

T = 7.76 s

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3 years ago

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