A substance with a define shape and volume is a

Find the position vector of a particle that has the given acceleration and the specified initial velocity and position. a(t) = 1

kondor19780726 [428]

Answer:

Explanation:

Given

Acceleration $a(t)=14t\hat{i]+\sin (t)\hat{j}+\cos (2t)\hat{k}$ [/tex]

and $v(0)=\hat{i}$

$r(0)=\hat{j}$

we know $a=\frac{\mathrm{d} v}{\mathrm{d} t}$

$\int dv=\int adt$

$v(t)=\int (14t\hat{i}+\sin (t)\hat{j}+\cos (2t)\hat{k})dt$

$v(t)=7t^2\hat{i}-\cos t\hat{j}+\frac{\sin (2t)\hat{k}}{2}+c$

at $t=0$

$v(0)=0-1\cdot \hat{j}+0+c$

$c=\hat{i}+\hat{j}$

$v(t)=(7t^2+1)\hat{i}+(1-\cos t)\hat{j}+\frac{\sin (2t)\hat{k}}{2}$

and $\frac{\mathrm{d} r}{\mathrm{d} t}=v(t)$

$\int dr=\int vdt$

$r(t)=\int ((7t^2+1)\hat{i}+(1-\cos t)\hat{j}+\frac{\sin (2t)\hat{k}}{2})dt$

$r(t)=(\frac{7}{2}t^3+t)\hat{i}+(t-\sin (t))\hat{j}+\frac{1}{2}\times (-\frac{1}{2}\cos 2t)\hat{k}+c_2$

at $t=0$

$r(0)=\hat{j}$

$r(t)=(\frac{7}{3}t^3+t)\hat{i}+(1+t-\sin t)\hat{j}+\frac{1}{4}(1-\cos 2t)\hat{k}$

4 0

3 years ago

If the mass of an object i if the mass of an object is 44 kg in its velocity is 10 m/s East how much kinetic energy

vampirchik [111]

K=0.5 mu×u
K=2200J no matter the direction

8 0

3 years ago

A 150kg person stands on a compression spring with spring constant 10, 000 N/m and norminal.Length of 0.50.What is the togal len

Eva8 [605]

Answer:

Total length of spring 0.647 m

Explanation:

We have given mass of the person m = 150 kg

Acceleration due to gravity $g=9.8m/sec^2$

Spring constant k = 10000 N/m

Nominal length of spring = 0.50

According to hook's law

$mg=kx$

$150\times 9.8=10000\times x$

x = 0.147 m

So total length of spring = 0.50+0.147 = 0.647 m

4 0

3 years ago

What makes sinkholes form?

skelet666 [1.2K]

Answer:

well for one it can be from drilling or when water starts to breck down the rocks

Explanation:

7 0

3 years ago

Read 2 more answers

A standing wave pattern is created on a string with mass density μ = 3.4 × 10-4 kg/m. A wave generator with frequency f = 61 Hz

uranmaximum [27]

Answer:

1) λ = 0.413 m , 2)v = 25,213 m / s , 3) T = 0.216 N , 4) m = 22.04 10-3 kg

Explanation:

1) The resonance occurs when the traveling wave bounces at the ends and the two waves are added, the ends as they are fixed have a node, the wavelength and the length of the string are related

λ = 2L / n n = 1, 2, 3 ...

In this case L = 0.62 m and n = 3

Let's calculate

λ = 2 0.62 / 3

λ = 0.413 m

2) the velocity related to wavelength and frequency

v = λ f

v = 0.413 61

v = 25,213 m / s

3) let's use the equation

v = √T /μ

T = v² μ

T = 25,213² 3.4 10⁻⁴

T = 0.216 N

4) the rope tension is proportional to the hanging weight

T-W = 0

T = W

W = m g

m = W / g

m = 0.216 / 9.8

m = 22.04 10-3 kg

5) n = 2

λ = 2 0.62 / 2

λ = 0.62 m

6) v = λ f

v = 0.62 61

v = 37.82 m / s

7) T = v² μ

T = 37.82² 3.4 10⁻⁴

T = 0.486 N

8) m = W / g

m = 0.486 / 9.8

m = 49.62 10⁻³ kg

9) n = 1

λ = 2 0.62

λ = 1.24 m

v = 1.24 61

v = 75.64 m / s

T = v² miu

T = 75.64² 3.4 10⁻⁴

T = 2.572 10⁻² N

m = 2.572 10⁻² / 9.8

m = 262.4 10⁻³ kg

5 0

3 years ago