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gulaghasi [49]
3 years ago
8

A particle moves according to a law of motion s = f(t), t ≥ 0, where t is measured in seconds and s in feet. f(t) = 0.01t4 − 0.0

2t3 (a) find the velocity at time t (in ft/s). v(t) = (b) what is the velocity after 1 second(s)? v(1) = ft/s (c) when is the particle at rest? t = s (smaller value) t = s (larger value)

Physics
1 answer:
masya89 [10]3 years ago
3 0
The distance (ft) traveled by the particle at time t (s) is
s(t) = 0.01 t⁴ - 0.02 t³

Part (a)
The velocity at time t is
v(t) = 0.04t³ - 0.06t²  ft/s

Part (b)
After 1 s, the velocity is
v(1) = 0.04 - 0.06 = - 0.02 ft/s

Part (c)
When the particle is at rest, the velocity is zero. The time when this happens is given by
0.04t³ - 0.06t² = 0
t²(0.04t - 0.06) = 0
The graph shown below presents a clear picture of the motion.

Answer:
t = 0 (smaller value) or t = 1.5 s (larger value)

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3 0
3 years ago
At the local playground, a 21-kg child sits on the right end of a horizontal teeter-totter, 1.8 m from the pivot point. On the l
Ksju [112]

Answer:

By convention a negative torque leads to clockwise rotation and a positive torque leads to counterclockwise rotation.

here weight of the child =21kgx9.8m/s2 = 205.8N

the torque exerted by the child Tc = - (1.8)(205.8) = -370.44N-m ,negative sign is inserted because this torque is clockwise and is therefore negative by convention.

torque exerted by adult Ta = 3(151) = 453N , counterclockwise torque.

net torque Tnet = -370.44+453 =82.56N , which is positive means counterclockwise rotation.

b) Ta = 2.5x151 = 377.5N-m

Tnet = -370.44+377.5 = 7.06N-m , positive ,counterclockwise rotation.

c)Ta = 2x151 = 302N-m

Tnet = -370.44+302 = -68.44N-m, negative,clockwise rotation.

5 0
3 years ago
Explain how we measure temperatures in our daily lives.
AnnyKZ [126]

Many devices have been invented to accurately measure temperature. It all started with the establishment of a temperature scale. This scale transformed the measurement of temperature into meaningful numbers.

In the early years of the eighteenth century, Gabriel Fahrenheit (1686-1736) created the Fahrenheit scale. He set the freezing point of water at 32 degrees and the boiling point at 212 degrees. These two points formed the anchors for his scale.


Later in that century, around 1743, Anders Celsius (1701-1744) invented the Celsius scale. Using the same anchor points, he determined the freezing temperature for water to be 0 degree and the boiling temperature 100 degrees. The Celsius scale is known as a Universal System Unit. It is used throughout science and in most countries.


There is a limit to how cold something can be. The Kelvin scale is designed to go to zero at this minimum temperature. The relationships between the different temperature scales are:



oK = 273.15 + oC        oC = (5/9)*(oF-32)        oF = (9/5)*oC+32


 oF oC oK

Water boils 212 100 373

Room Temperature 72 23 296

Water Freezes 32 0 273

Absolute Zero -460 -273 0

At a temperature of Absolute Zero there is no motion and no heat. Absolute zero is where all atomic and molecular motion stops and is the lowest temperature possible. Absolute Zero occurs at 0 degrees Kelvin or -273.15 degrees Celsius or at -460 degrees Fahrenheit. All objects emit thermal energy or heat unless they have a temperature of absolute zero.


If we want to understand what temperature means on the molecular level, we should remember that temperature is the average energy of the molecules that composes a substance. The atoms and molecules in a substance do not always travel at the same speed. This means that there is a range of energy (the energy of motion) among the molecules. In a gas, for example, the molecules are traveling in random directions at a variety of speeds - some are fast and some are slow. Sometimes these molecules collide with each other. When this happens the higher speed molecule transfers some of its energy to the slower molecule causing the slower molecule to speed up and the faster molecule to slow down. If more energy is put into the system, the average speed of the molecules will increase and more thermal energy or heat will be produced. So, higher temperatures mean a substance has higher average molecular motion. We do not feel or detect a bunch of different temperatures for each molecule which has a different speed. What we measure as the temperature is always related to the average speed of the molecules in a system

3 0
3 years ago
An athlete stretches a spring an extra 40.0 cm beyond its initial length. How much energy has he transferred to the spring, if t
notsponge [240]

Answer:

<h2>b) 4230 J </h2>

Explanation:

Step one:

given data

extension= 40cm

Spring constant K= 52.9N/cm

Step two:

Required

the Kinetic Energy KE

the expression to find the kinetic energy is

KE= 1/2ke^2

substituting our data we have

KE= 1/2*52.9*40^2

KE=0.5*52.9*1600

KE= 42320Joules

<u>The answer is b) 4230 J </u>

4 0
3 years ago
You are visiting your friend Fabio's house. You find that, as a joke, he filled his swimming pool with Kool-Aid, which dissolved
oksian1 [2.3K]

Answer:

Explanation:

The volume of contaminated water

= cross sectional area x height of water level

3.14 x 9 x 9 x 7.5 ft³

= 1907.55 ft³

mass = density x volume

= 1907.55 x 63.5 lbs

m = 121129.425 lbs

This mass has to be raised to the height of 8 ft before evacuation .

There is a rise of centre of mass of

8 - 7.5/2 ft

h = 4.25 ft

Energy required

= mgh

= 121129.425 x 32 x 4.25

= 16473601.8 unit.

3 0
3 years ago
Read 2 more answers
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