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DanielleElmas [232]

2 years ago

6

The displacement of a car is a function of time as follows: x(t)=25+3.0t², with x is in meters. Find the average velocity betwee

n t1 = 1.0s and t2 = 4.0s.

1 answer:

aniked [119]2 years ago

5 0

Answer: 15m/s

Explanation: <u>Average</u> <u>Velocity</u> is vector describing the total displacement of an object and the time taken to change its position. It is represented as:

$v=\frac{\Delta x}{\Delta t}$

At t₁ = 1.0s, displacement x₁ is:

$x(1)=25+3(1)^{2}$

x(1) = 28

At t₂ = 4.0s:

$x(4)=25+3(4)^{2}$

x(4) = 73

Then, average speed is

$v=\frac{73-28}{4-1}$

v = 15

The average velocity of a car between t₁ = 1s and t₂ = 4s is 15m/s

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When the play button is pressed, a CD accelerates uniformly from rest to 450 rev/min in 3.0 revolutions. If the CD has a radius

Marina CMI [18]

To solve this problem it is necessary to apply the kinematic equations of angular motion.

Torque from the rotational movement is defined as

$\tau = I\alpha$

where

I = Moment of inertia $\rightarrow \frac{1}{2}mr^2$ For a disk

$\alpha =$ Angular acceleration

The angular acceleration at the same time can be defined as function of angular velocity and angular displacement (Without considering time) through the expression:

$2 \alpha \theta = \omega_f^2-\omega_i^2$

Where

$\omega_{f,i} =$ Final and Initial Angular velocity

$\alpha =$ Angular acceleration

$\theta =$ Angular displacement

Our values are given as

$\omega_i = 0 rad/s$

$\omega_f = 450rev/min (\frac{1min}{60s})(\frac{2\pi rad}{1rev})$

$\omega_f = 47.12rad/s$

$\theta = 3 rev (\frac{2\pi rad}{1rev}) \rightarrow 6\pi rad$

$r = 7cm = 7*10^{-2}m$

$m = 17g = 17*10^{-3}kg$

Using the expression of angular acceleration we can find the to then find the torque, that is,

$2\alpha\theta=\omega_f^2-\omega_i^2$

$\alpha=\frac{\omega_f^2-\omega_i^2}{2\theta}$

$\alpha = \frac{47.12^2-0^2}{2*6\pi}$

$\alpha = 58.89rad/s^2$

With the expression of the acceleration found it is now necessary to replace it on the torque equation and the respective moment of inertia for the disk, so

$\tau = I\alpha$

$\tau = (\frac{1}{2}mr^2)\alpha$

$\tau = (\frac{1}{2}(17*10^{-3})(7*10^{-2})^2)(58.89)$

$\tau = 0.00245N\cdot m \approx 2.45*10^{-3}N\cdot m$

Therefore the torque exerted on it is $2.45*10^{-3}N\cdot m$

3 0

2 years ago

If there is a huge boulder on your lawn and you want to determine its density, but it is

Olin [163]

There are different options here but all of them work by approximating and assuming.

i) that the boulder is above ground.

ii) that the bottom surface of the boulder is known.

iii) the shape of the boulder is taken into account.

The most accurate way is measuring it by displacement method but the boulder is immovable hence the volume can be calculated by measuring the boulder or a waterproof box to be built around the boulder and calculate the volume occupied by boulder.

All the above methods are estimating methods.

*Another way to find the density is through specific gravity.

S.G = <u>Density</u><u> </u><u>of</u><u> </u><u>object</u>

Density of water

If the material that makes the boulder is known that is if it's stone or a mineral then the specific gravity can be found.

If the boulder is purely rock then S.G lies between 3 - 3.5 and the density of water is known thus the density of the boulder can be found without moving the boulder.

This is what I think after correction and allthe best!

3 0

1 year ago

Read 2 more answers

A crane raises a crate with a mass of 150 kg to a height of 20 m. Given that

Virty [35]

Answer:

$\boxed {\boxed {\sf 29,400 \ Joules}}$

Explanation:

Gravitational potential energy is the energy an object possesses due to its position. It is the product of mass, height, and acceleration due to gravity.

$E_P= m \times g \times h$

The object has a mass of 150 kilograms and is raised to a height of 20 meters. Since this is on Earth, the acceleration due to gravity is 9.8 meters per square second.

m= 150 kg
g= 9.8 m/s²
h= 20 m

Substitute the values into the formula.

$E_p= 150 \ kg \times 9.8 \ m/s^2 \times 20 \ m$

Multiply the three numbers and their units together.

$E_p=1470 \ kg*m/s^2 \times 20 m$

$E_p=29400 \ kg*m^2/s^2$

Convert the units.

1 kilogram meter square per second squared (1 kg *m²/s²) is equal to 1 Joule (J). Our answer of 29,400 kg*m²/s² is equal to 29,400 Joules.

$E_p= 29,400 \ J$

The crate has <u>29,400 Joules</u> of potential energy.

7 0

2 years ago

A 2-kg toy car accelerates from 5 to 10 m/s.

andre [41]

<h3><u>Full Question:</u></h3>

A 2-kg toy car accelerates from 5 to 10 m/s in 2 seconds. Find the applied force.

<h2><u>Answer:</u></h2>

Force applied is $5\frac {kgm} {s^2}$ .

<h3><u>Explanation:</u></h3>

Force is defined as something which changes or tends to change the velocity of a body. And acceleration is defined as the rate of change of velocity of a body per time. Both of them are vector quantities.

The initial velocity of the body = 5 m/s.

The final velocity of the body = 10 m/s.

So the change in velocity = 10 - 5 m/s = 5m/s.

Time period = 2 seconds.

So acceleration = $\frac52 m/s^2$ = $2.5 m/s^2$

The force is defined as the product of mass and acceleration of the body.

Mass of body = 2 kg.

So, force applied = $2 \times 2.5 kgm/s^2$ . = $5kgm/s^2$ .

4 0

2 years ago

Question 6 Unsaved How many neutrons does element X have if its atomic number is 29 and its mass number is 84? Your Answer:

belka [17]

84-29=55 neutrons in nucleus

3 0

2 years ago