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Pavel [41]
3 years ago
7

Consider a particle moving along the x-axis where x(t) is the position of the particle at time t, x' (t) is its velocity, and x'

' (t) is its acceleration. x(t) = t3 − 12t2 + 21t − 9, 0 ≤ t ≤ 10 (a) Find the velocity and acceleration of the particle.
Physics
1 answer:
nignag [31]3 years ago
5 0

The position of the particle is given by:

x(t) = t³ - 12t² + 21t - 9

Differentiate x(t) with respect to t to find the velocity x'(t):

x'(t) = 3t² - 24t + 21

Differentiate x'(t) with respect to t to find the acceleration x''(t):

x''(t) = 6t - 24

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My name is Ann [436]

Answer:

1. 13..6 grams per centimeters cubed.

2. Mass = 400kg

3. Volume = 200cm = 2m

Explanation:

1. The conversion for kg/m^3 to g/cm^3 is divide by 1000.

2. density=\frac{mass}{volume}

1000=\frac{mass}{2 * 1 * 0.2}

1000*0.4=mass

400kg = mass

3. density=\frac{mass}{volume}

0.6=\frac{120}{volume}

volume=\frac{120}{0.6}

volume= 200cm

4 0
2 years ago
If a 75-kg skater starts his skate at 8.0m, at his lowest point (height = 0), what is
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6 0
3 years ago
A pilot heads his jet due east. The jet has a speed of 475 mi/h relative to the air. The wind is blowing due north with a speed
oksian1 [2.3K]

Explanation:

a. The velocity of the wind as a vector in component form will be represented as v vector:

    v=30j

b.The velocity of the jet relative to the air as a vector in component form will be represented as u vector

    u=475i

c. The true velocity of the jet as a vector will be represented as w:

  w=u+v

  w=475i+30j

d.  The true speed of the jet will be calculated as:

    IwI=\sqrt{(475)^2+(30)^2}

    IwI=\sqrt{225625+900}

    IwI=\sqrt{226525}

    IwI=476 mi/h

e. The direction of the jet will be:

tita=tan^{-1}\frac{30}{475}

tita=tan^{-1}(0.0632)

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7 0
3 years ago
The diameter of Earth (to two significant figures) is 7900 miles. Calculate its circumference.
Bess [88]

Answer:

The circumference of the Earth is 24818.58 miles

Explanation:

Analysis conceptual : The formula of the circumference is the following:

L= π*D Formula (1)

Where:

L : is the length of the circumference in miles (mi)

π : is the constant

D : is the diameter of the circumference in miles (mi)

Known data

π = 3.1416

D= 7900 miles:  Diameter of the Earth

Problem development

We apply the formula 1 to calculate the circumference of the Earth  (L):

L= π*7900 miles

L= 24818.58 miles

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